Løs 20(1+2x/100)*25*20*(1-3x/10div100)+5(1+6x/100)*4*20*(1-x/4div100)=(20*(1+2xdiv100)*25+5*(1+6xdiv100)*4)*20*(1-5xdiv18div100)

$$20(1+ \frac{ 2x }{ 100 } ) \times 25 \times 20 \times (1- \frac{ 3x }{ 10 } \div 100)+5(1+ \frac{ 6x }{ 100 } ) \times 4 \times 20 \times (1- \frac{ x }{ 4 } \div 100)=(20 \times (1+2x \div 100) \times 25+5 \times (1+6x \div 100) \times 4) \times 20 \times (1-5x \div 18 \div 100)$$

Løs for x

$$x = -\frac{950}{17} = -55\frac{15}{17} \approx -55,882352941$$

$$x=0$$

Fremgangsmåten ved bruk av andregradsformelen

Multipliser begge sider av ligningen med 100.

$$2000\left(1+\frac{2x}{100}\right)\times 25\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 2x på 100 for å få \frac{1}{50}x.

$$2000\left(1+\frac{1}{50}x\right)\times 25\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 25 for å få 50000.

$$50000\left(1+\frac{1}{50}x\right)\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 50000 med 20 for å få 1000000.

$$1000000\left(1+\frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 1000000 med 1+\frac{1}{50}x.

$$\left(1000000+1000000\times \frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 1000000 med \frac{1}{50} for å få \frac{1000000}{50}.

$$\left(1000000+\frac{1000000}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 1000000 på 50 for å få 20000.

$$\left(1000000+20000x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 1000000+20000x med hvert ledd i 1-\frac{\frac{3x}{10}}{100}.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 6x på 100 for å få \frac{3}{50}x.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{3}{50}x\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 500 med 4 for å få 2000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+2000\left(1+\frac{3}{50}x\right)\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 20 for å få 40000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(1+\frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 40000 med 1+\frac{3}{50}x.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+40000\times \frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 40000\times \frac{3}{50} som en enkelt brøk.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{40000\times 3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 40000 med 3 for å få 120000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{120000}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 120000 på 50 for å få 2400.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+2400x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 40000+2400x med hvert ledd i 1-\frac{\frac{x}{4}}{100}.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Legg sammen 1000000 og 40000 for å få 1040000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Kombiner 20000x og 2400x for å få 22400x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 2x på 100 for å få \frac{1}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{1}{50}x\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 20 med 25 for å få 500.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500\left(1+\frac{1}{50}x\right)+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 500 med 1+\frac{1}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+500\times \frac{1}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 500 med \frac{1}{50} for å få \frac{500}{50}.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+\frac{500}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 500 på 50 for å få 10.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 6x på 100 for å få \frac{3}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+5\left(1+\frac{3}{50}x\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 5 med 4 for å få 20.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20\left(1+\frac{3}{50}x\right)\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 20 med 1+\frac{3}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+20\times \frac{3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 20\times \frac{3}{50} som en enkelt brøk.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{20\times 3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 20 med 3 for å få 60.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{60}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Forkort brøken \frac{60}{50} til minste felles nevner ved å dele teller og nevner på 10.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Legg sammen 500 og 20 for å få 520.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(520+10x+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Kombiner 10x og \frac{6}{5}x for å få \frac{56}{5}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(520+\frac{56}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 100 med 20 for å få 2000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=2000\left(520+\frac{56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 2000 med 520+\frac{56}{5}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+2000\times \frac{56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 2000\times \frac{56}{5} som en enkelt brøk.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+\frac{2000\times 56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 56 for å få 112000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+\frac{112000}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 112000 på 5 for å få 22400.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+22400x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 1040000+22400x med hvert ledd i 1-\frac{\frac{5x}{18}}{100}.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=1040000+1040000\left(-\frac{\frac{5x}{18}}{100}\right)+22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 1040000 fra begge sider.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000=1040000\left(-\frac{\frac{5x}{18}}{100}\right)+22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 1040000 fra 1040000 for å få 0.

$$1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=1040000\left(-\frac{\frac{5x}{18}}{100}\right)+22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 1040000\left(-\frac{\frac{5x}{18}}{100}\right) fra begge sider.

$$1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)=22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 22400x fra begge sider.

$$1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x=22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 22400x\left(-\frac{\frac{5x}{18}}{100}\right) fra begge sider.

$$1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x-22400x\left(-\frac{\frac{5x}{18}}{100}\right)=0$$

Multipliser begge sider av ligningen med 100.

$$100\left(1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x\right)-2240000x\left(-\frac{\frac{5x}{18}}{100}\right)=0$$

Endre rekkefølgen på leddene.

$$100\left(2400x\left(-\frac{x}{4\times 100}\right)+20000x\left(-\frac{3x}{10\times 100}\right)+40000\left(-\frac{x}{4\times 100}\right)+1000000\left(-\frac{3x}{10\times 100}\right)+22400x-1040000\left(-\frac{5x}{18\times 100}\right)-22400x\right)-2240000x\left(-\frac{5x}{18\times 100}\right)=0$$

Multipliser 40000 med -1 for å få -40000. Multipliser 1000000 med -1 for å få -1000000. Multipliser -1 med 1040000 for å få -1040000.

$$100\left(2400x\left(-1\right)\times \frac{x}{4\times 100}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 2400 med -1 for å få -2400.

$$100\left(-2400x\times \frac{x}{4\times 100}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 4 med 100 for å få 400.

$$100\left(-2400x\times \frac{x}{400}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Opphev den største felles faktoren 400 i 2400 og 400.

$$100\left(-6xx+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 20000 med -1 for å få -20000.

$$100\left(-6xx-20000x\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 10 med 100 for å få 1000.

$$100\left(-6xx-20000x\times \frac{3x}{1000}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Opphev den største felles faktoren 1000 i 20000 og 1000.

$$100\left(-6xx-20\times 3xx-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 4 med 100 for å få 400.

$$100\left(-6xx-20\times 3xx-40000\times \frac{x}{400}-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Opphev den største felles faktoren 400 i 40000 og 400.

$$100\left(-6xx-20\times 3xx-100x-1000000\times \frac{3x}{10\times 100}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 10 med 100 for å få 1000.

$$100\left(-6xx-20\times 3xx-100x-1000000\times \frac{3x}{1000}+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Opphev den største felles faktoren 1000 i 1000000 og 1000.

$$100\left(-6xx-20\times 3xx-100x-1000\times 3x+22400x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Kombiner -100x og 22400x for å få 22300x.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser -1040000 med -1 for å få 1040000.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Eliminer 5 i både teller og nevner.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000\times \frac{x}{18\times 20}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 18 med 20 for å få 360.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000\times \frac{x}{360}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Uttrykk 1040000\times \frac{x}{360} som en enkelt brøk.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+\frac{1040000x}{360}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Kombiner 22300x og -22400x for å få -100x.

$$100\left(-6xx-20\times 3xx-100x-1000\times 3x+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser -20 med 3 for å få -60. Multipliser -1000 med 3 for å få -3000.

$$100\left(-6xx-60xx-100x-3000x+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Kombiner -6xx og -60xx for å få -66xx.

$$100\left(-66xx-100x-3000x+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Kombiner -100x og -3000x for å få -3100x.

$$100\left(-66xx-3100x+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Bruk den distributive lov til å multiplisere 100 med -66xx-3100x+\frac{1040000x}{360}.

$$-6600x^{2}-310000x+100\times \frac{1040000x}{360}-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Del 1040000x på 360 for å få \frac{26000}{9}x.

$$-6600x^{2}-310000x+100\times \frac{26000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Uttrykk 100\times \frac{26000}{9} som en enkelt brøk.

$$-6600x^{2}-310000x+\frac{100\times 26000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser 100 med 26000 for å få 2600000.

$$-6600x^{2}-310000x+\frac{2600000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Kombiner -310000x og \frac{2600000}{9}x for å få -\frac{190000}{9}x.

$$-6600x^{2}-\frac{190000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multipliser -2240000 med -1 for å få 2240000.

$$-6600x^{2}-\frac{190000}{9}x+2240000x\times \frac{5x}{18\times 100}=0$$

Eliminer 5 i både teller og nevner.

$$-6600x^{2}-\frac{190000}{9}x+2240000x\times \frac{x}{18\times 20}=0$$

Multipliser 18 med 20 for å få 360.

$$-6600x^{2}-\frac{190000}{9}x+2240000x\times \frac{x}{360}=0$$

Uttrykk 2240000\times \frac{x}{360} som en enkelt brøk.

$$-6600x^{2}-\frac{190000}{9}x+\frac{2240000x}{360}x=0$$

Del 2240000x på 360 for å få \frac{56000}{9}x.

$$-6600x^{2}-\frac{190000}{9}x+\frac{56000}{9}xx=0$$

Multipliser x med x for å få x^{2}.

$$-6600x^{2}-\frac{190000}{9}x+\frac{56000}{9}x^{2}=0$$

Kombiner -6600x^{2} og \frac{56000}{9}x^{2} for å få -\frac{3400}{9}x^{2}.

$$-\frac{3400}{9}x^{2}-\frac{190000}{9}x=0$$

Denne ligningen er i standard form: ax^{2}+bx+c=0. Sett inn -\frac{3400}{9} for a, -\frac{190000}{9} for b og 0 for c i andregradsformelen, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{190000}{9}\right)±\sqrt{\left(-\frac{190000}{9}\right)^{2}}}{2\left(-\frac{3400}{9}\right)}$$

Ta kvadratroten av \left(-\frac{190000}{9}\right)^{2}.

$$x=\frac{-\left(-\frac{190000}{9}\right)±\frac{190000}{9}}{2\left(-\frac{3400}{9}\right)}$$

Det motsatte av -\frac{190000}{9} er \frac{190000}{9}.

$$x=\frac{\frac{190000}{9}±\frac{190000}{9}}{2\left(-\frac{3400}{9}\right)}$$

Multipliser 2 ganger -\frac{3400}{9}.

$$x=\frac{\frac{190000}{9}±\frac{190000}{9}}{-\frac{6800}{9}}$$

Nå kan du løse formelen x=\frac{\frac{190000}{9}±\frac{190000}{9}}{-\frac{6800}{9}} når ± er pluss. Legg sammen \frac{190000}{9} og \frac{190000}{9} ved å finne en fellesnevner og legge sammen tellerne. Forkort deretter brøken om mulig.

$$x=\frac{\frac{380000}{9}}{-\frac{6800}{9}}$$

Del \frac{380000}{9} på -\frac{6800}{9} ved å multiplisere \frac{380000}{9} med den resiproke verdien av -\frac{6800}{9}.

$$x=-\frac{950}{17}$$

Nå kan du løse formelen x=\frac{\frac{190000}{9}±\frac{190000}{9}}{-\frac{6800}{9}} når ± er minus. Trekk fra \frac{190000}{9} fra \frac{190000}{9} ved å finne en fellesnevner og trekke fra tellerne. Forkort deretter brøken om mulig.

$$x=\frac{0}{-\frac{6800}{9}}$$

Del 0 på -\frac{6800}{9} ved å multiplisere 0 med den resiproke verdien av -\frac{6800}{9}.

$$x=0$$

Ligningen er nå løst.

$$x=-\frac{950}{17} x=0$$

Trinn for å fullføre kvadreringen

Multipliser begge sider av ligningen med 100.

$$2000\left(1+\frac{2x}{100}\right)\times 25\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 2x på 100 for å få \frac{1}{50}x.

$$2000\left(1+\frac{1}{50}x\right)\times 25\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 25 for å få 50000.

$$50000\left(1+\frac{1}{50}x\right)\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 50000 med 20 for å få 1000000.

$$1000000\left(1+\frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 1000000 med 1+\frac{1}{50}x.

$$\left(1000000+1000000\times \frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 1000000 med \frac{1}{50} for å få \frac{1000000}{50}.

$$\left(1000000+\frac{1000000}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 1000000 på 50 for å få 20000.

$$\left(1000000+20000x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 1000000+20000x med hvert ledd i 1-\frac{\frac{3x}{10}}{100}.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 6x på 100 for å få \frac{3}{50}x.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{3}{50}x\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 500 med 4 for å få 2000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+2000\left(1+\frac{3}{50}x\right)\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 20 for å få 40000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(1+\frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 40000 med 1+\frac{3}{50}x.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+40000\times \frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 40000\times \frac{3}{50} som en enkelt brøk.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{40000\times 3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 40000 med 3 for å få 120000.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{120000}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 120000 på 50 for å få 2400.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+2400x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 40000+2400x med hvert ledd i 1-\frac{\frac{x}{4}}{100}.

$$1000000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Legg sammen 1000000 og 40000 for å få 1040000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+20000x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Kombiner 20000x og 2400x for å få 22400x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 2x på 100 for å få \frac{1}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{1}{50}x\right)\times 25+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 20 med 25 for å få 500.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500\left(1+\frac{1}{50}x\right)+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 500 med 1+\frac{1}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+500\times \frac{1}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 500 med \frac{1}{50} for å få \frac{500}{50}.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+\frac{500}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 500 på 50 for å få 10.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 6x på 100 for å få \frac{3}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+5\left(1+\frac{3}{50}x\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 5 med 4 for å få 20.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20\left(1+\frac{3}{50}x\right)\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 20 med 1+\frac{3}{50}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+20\times \frac{3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 20\times \frac{3}{50} som en enkelt brøk.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{20\times 3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 20 med 3 for å få 60.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{60}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Forkort brøken \frac{60}{50} til minste felles nevner ved å dele teller og nevner på 10.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(500+10x+20+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Legg sammen 500 og 20 for å få 520.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(520+10x+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Kombiner 10x og \frac{6}{5}x for å få \frac{56}{5}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(520+\frac{56}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 100 med 20 for å få 2000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=2000\left(520+\frac{56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov til å multiplisere 2000 med 520+\frac{56}{5}x.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+2000\times \frac{56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Uttrykk 2000\times \frac{56}{5} som en enkelt brøk.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+\frac{2000\times 56}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multipliser 2000 med 56 for å få 112000.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+\frac{112000}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Del 112000 på 5 for å få 22400.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(1040000+22400x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Bruk den distributive lov ved å multiplisere hvert ledd i 1040000+22400x med hvert ledd i 1-\frac{\frac{5x}{18}}{100}.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=1040000+1040000\left(-\frac{\frac{5x}{18}}{100}\right)+22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 1040000\left(-\frac{\frac{5x}{18}}{100}\right) fra begge sider.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)=1040000+22400x+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 22400x fra begge sider.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x=1040000+22400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Trekk fra 22400x\left(-\frac{\frac{5x}{18}}{100}\right) fra begge sider.

$$1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x-22400x\left(-\frac{\frac{5x}{18}}{100}\right)=1040000$$

Multipliser begge sider av ligningen med 100.

$$100\left(1040000+1000000\left(-\frac{\frac{3x}{10}}{100}\right)+22400x+20000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-1040000\left(-\frac{\frac{5x}{18}}{100}\right)-22400x\right)-2240000x\left(-\frac{\frac{5x}{18}}{100}\right)=104000000$$

Endre rekkefølgen på leddene.

$$100\left(2400x\left(-\frac{x}{4\times 100}\right)+20000x\left(-\frac{3x}{10\times 100}\right)+40000\left(-\frac{x}{4\times 100}\right)+1000000\left(-\frac{3x}{10\times 100}\right)+22400x+1040000-1040000\left(-\frac{5x}{18\times 100}\right)-22400x\right)-2240000x\left(-\frac{5x}{18\times 100}\right)=104000000$$

Multipliser 40000 med -1 for å få -40000. Multipliser 1000000 med -1 for å få -1000000. Multipliser -1 med 1040000 for å få -1040000.

$$100\left(2400x\left(-1\right)\times \frac{x}{4\times 100}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 2400 med -1 for å få -2400.

$$100\left(-2400x\times \frac{x}{4\times 100}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 4 med 100 for å få 400.

$$100\left(-2400x\times \frac{x}{400}+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Opphev den største felles faktoren 400 i 2400 og 400.

$$100\left(-6xx+20000x\left(-1\right)\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 20000 med -1 for å få -20000.

$$100\left(-6xx-20000x\times \frac{3x}{10\times 100}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 10 med 100 for å få 1000.

$$100\left(-6xx-20000x\times \frac{3x}{1000}-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Opphev den største felles faktoren 1000 i 20000 og 1000.

$$100\left(-6xx-20\times 3xx-40000\times \frac{x}{4\times 100}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 4 med 100 for å få 400.

$$100\left(-6xx-20\times 3xx-40000\times \frac{x}{400}-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Opphev den største felles faktoren 400 i 40000 og 400.

$$100\left(-6xx-20\times 3xx-100x-1000000\times \frac{3x}{10\times 100}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 10 med 100 for å få 1000.

$$100\left(-6xx-20\times 3xx-100x-1000000\times \frac{3x}{1000}+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Opphev den største felles faktoren 1000 i 1000000 og 1000.

$$100\left(-6xx-20\times 3xx-100x-1000\times 3x+22400x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Kombiner -100x og 22400x for å få 22300x.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000-1040000\left(-1\right)\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser -1040000 med -1 for å få 1040000.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000+1040000\times \frac{5x}{18\times 100}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Eliminer 5 i både teller og nevner.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000+1040000\times \frac{x}{18\times 20}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 18 med 20 for å få 360.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000+1040000\times \frac{x}{360}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Uttrykk 1040000\times \frac{x}{360} som en enkelt brøk.

$$100\left(-6xx-20\times 3xx+22300x-1000\times 3x+1040000+\frac{1040000x}{360}-22400x\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Kombiner 22300x og -22400x for å få -100x.

$$100\left(-6xx-20\times 3xx-100x-1000\times 3x+1040000+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser -20 med 3 for å få -60. Multipliser -1000 med 3 for å få -3000.

$$100\left(-6xx-60xx-100x-3000x+1040000+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Kombiner -6xx og -60xx for å få -66xx.

$$100\left(-66xx-100x-3000x+1040000+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Kombiner -100x og -3000x for å få -3100x.

$$100\left(-66xx-3100x+1040000+\frac{1040000x}{360}\right)-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Bruk den distributive lov til å multiplisere 100 med -66xx-3100x+1040000+\frac{1040000x}{360}.

$$-6600x^{2}-310000x+104000000+100\times \frac{1040000x}{360}-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Del 1040000x på 360 for å få \frac{26000}{9}x.

$$-6600x^{2}-310000x+104000000+100\times \frac{26000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Uttrykk 100\times \frac{26000}{9} som en enkelt brøk.

$$-6600x^{2}-310000x+104000000+\frac{100\times 26000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser 100 med 26000 for å få 2600000.

$$-6600x^{2}-310000x+104000000+\frac{2600000}{9}x-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Kombiner -310000x og \frac{2600000}{9}x for å få -\frac{190000}{9}x.

$$-6600x^{2}-\frac{190000}{9}x+104000000-2240000x\left(-1\right)\times \frac{5x}{18\times 100}=104000000$$

Multipliser -2240000 med -1 for å få 2240000.

$$-6600x^{2}-\frac{190000}{9}x+104000000+2240000x\times \frac{5x}{18\times 100}=104000000$$

Eliminer 5 i både teller og nevner.

$$-6600x^{2}-\frac{190000}{9}x+104000000+2240000x\times \frac{x}{18\times 20}=104000000$$

Multipliser 18 med 20 for å få 360.

$$-6600x^{2}-\frac{190000}{9}x+104000000+2240000x\times \frac{x}{360}=104000000$$

Uttrykk 2240000\times \frac{x}{360} som en enkelt brøk.

$$-6600x^{2}-\frac{190000}{9}x+104000000+\frac{2240000x}{360}x=104000000$$

Del 2240000x på 360 for å få \frac{56000}{9}x.

$$-6600x^{2}-\frac{190000}{9}x+104000000+\frac{56000}{9}xx=104000000$$

Multipliser x med x for å få x^{2}.

$$-6600x^{2}-\frac{190000}{9}x+104000000+\frac{56000}{9}x^{2}=104000000$$

Kombiner -6600x^{2} og \frac{56000}{9}x^{2} for å få -\frac{3400}{9}x^{2}.

$$-\frac{3400}{9}x^{2}-\frac{190000}{9}x+104000000=104000000$$

Trekk fra 104000000 fra begge sider.

$$-\frac{3400}{9}x^{2}-\frac{190000}{9}x=104000000-104000000$$

Trekk fra 104000000 fra 104000000 for å få 0.

$$-\frac{3400}{9}x^{2}-\frac{190000}{9}x=0$$

Del begge sidene av ligningen på -\frac{3400}{9}, som er det samme som å multiplisere begge sidene med den resiproke verdien av brøken.

$$\frac{-\frac{3400}{9}x^{2}-\frac{190000}{9}x}{-\frac{3400}{9}}=\frac{0}{-\frac{3400}{9}}$$

Hvis du deler på -\frac{3400}{9}, gjør du om gangingen med -\frac{3400}{9}.

$$x^{2}+\left(-\frac{\frac{190000}{9}}{-\frac{3400}{9}}\right)x=\frac{0}{-\frac{3400}{9}}$$

Del -\frac{190000}{9} på -\frac{3400}{9} ved å multiplisere -\frac{190000}{9} med den resiproke verdien av -\frac{3400}{9}.

$$x^{2}+\frac{950}{17}x=\frac{0}{-\frac{3400}{9}}$$

Del 0 på -\frac{3400}{9} ved å multiplisere 0 med den resiproke verdien av -\frac{3400}{9}.

$$x^{2}+\frac{950}{17}x=0$$

Del \frac{950}{17}, koeffisienten i x termen, etter 2 for å få \frac{475}{17}. Deretter legger du til kvadrat firkanten av \frac{475}{17} på begge sider av ligningen. Dette trinnet gjør venstre side av ligningen til en perfekt firkant.

$$x^{2}+\frac{950}{17}x+\left(\frac{475}{17}\right)^{2}=\left(\frac{475}{17}\right)^{2}$$

Kvadrer \frac{475}{17} ved å kvadrere både telleren og nevneren i brøken.

$$x^{2}+\frac{950}{17}x+\frac{225625}{289}=\frac{225625}{289}$$

Faktoriser x^{2}+\frac{950}{17}x+\frac{225625}{289}. Generelt, når x^{2}+bx+c er et kvadrattall, kan det alltid faktoriseres som \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{475}{17}\right)^{2}=\frac{225625}{289}$$

Ta kvadratroten av begge sider av ligningen.

$$\sqrt{\left(x+\frac{475}{17}\right)^{2}}=\sqrt{\frac{225625}{289}}$$

Forenkle.

$$x+\frac{475}{17}=\frac{475}{17} x+\frac{475}{17}=-\frac{475}{17}$$

Trekk fra \frac{475}{17} fra begge sider av ligningen.

$$x=0 x=-\frac{950}{17}$$