Solve 20(1+2x/100)*2.5*20*(1-3x/10div100)+5(1+6x/100)*4*20*(1-x/4div100)=(20*(1+2xdiv100)*2.5+5*(1+6xdiv100)*4)*20*(1-5xdiv18div100)

$$20(1+ \frac{ 2x }{ 100 } ) \times 2.5 \times 20 \times (1- \frac{ 3x }{ 10 } \div 100)+5(1+ \frac{ 6x }{ 100 } ) \times 4 \times 20 \times (1- \frac{ x }{ 4 } \div 100)=(20 \times (1+2x \div 100) \times 2.5+5 \times (1+6x \div 100) \times 4) \times 20 \times (1-5x \div 18 \div 100)$$

Solve for x

$$x=50$$

$$x=0$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 100.

$$2000\left(1+\frac{2x}{100}\right)\times 2.5\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 2x by 100 to get \frac{1}{50}x.

$$2000\left(1+\frac{1}{50}x\right)\times 2.5\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 2.5 to get 5000.

$$5000\left(1+\frac{1}{50}x\right)\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 5000 and 20 to get 100000.

$$100000\left(1+\frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 100000 by 1+\frac{1}{50}x.

$$\left(100000+100000\times \frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 100000 and \frac{1}{50} to get \frac{100000}{50}.

$$\left(100000+\frac{100000}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 100000 by 50 to get 2000.

$$\left(100000+2000x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 100000+2000x by each term of 1-\frac{\frac{3x}{10}}{100}.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 6x by 100 to get \frac{3}{50}x.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{3}{50}x\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 500 and 4 to get 2000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+2000\left(1+\frac{3}{50}x\right)\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 20 to get 40000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(1+\frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 40000 by 1+\frac{3}{50}x.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+40000\times \frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 40000\times \frac{3}{50} as a single fraction.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{40000\times 3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 40000 and 3 to get 120000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{120000}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 120000 by 50 to get 2400.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+2400x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 40000+2400x by each term of 1-\frac{\frac{x}{4}}{100}.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Add 100000 and 40000 to get 140000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Combine 2000x and 2400x to get 4400x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 2x by 100 to get \frac{1}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{1}{50}x\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 20 and 2.5 to get 50.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50\left(1+\frac{1}{50}x\right)+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 50 by 1+\frac{1}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+50\times \frac{1}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Cancel out 50 and 50.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 6x by 100 to get \frac{3}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+5\left(1+\frac{3}{50}x\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 5 and 4 to get 20.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20\left(1+\frac{3}{50}x\right)\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 20 by 1+\frac{3}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+20\times \frac{3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 20\times \frac{3}{50} as a single fraction.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{20\times 3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 20 and 3 to get 60.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{60}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Reduce the fraction \frac{60}{50} to lowest terms by extracting and canceling out 10.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Add 50 and 20 to get 70.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(70+x+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Combine x and \frac{6}{5}x to get \frac{11}{5}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(70+\frac{11}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 100 and 20 to get 2000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=2000\left(70+\frac{11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 2000 by 70+\frac{11}{5}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+2000\times \frac{11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 2000\times \frac{11}{5} as a single fraction.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+\frac{2000\times 11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 11 to get 22000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+\frac{22000}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 22000 by 5 to get 4400.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+4400x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 140000+4400x by each term of 1-\frac{\frac{5x}{18}}{100}.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=140000+140000\left(-\frac{\frac{5x}{18}}{100}\right)+4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 140000 from both sides.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000=140000\left(-\frac{\frac{5x}{18}}{100}\right)+4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 140000 from 140000 to get 0.

$$100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=140000\left(-\frac{\frac{5x}{18}}{100}\right)+4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 140000\left(-\frac{\frac{5x}{18}}{100}\right) from both sides.

$$100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)=4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 4400x from both sides.

$$100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x=4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 4400x\left(-\frac{\frac{5x}{18}}{100}\right) from both sides.

$$100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x-4400x\left(-\frac{\frac{5x}{18}}{100}\right)=0$$

Multiply both sides of the equation by 100.

$$100\left(100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x\right)-440000x\left(-\frac{\frac{5x}{18}}{100}\right)=0$$

Reorder the terms.

$$100\left(2000x\left(-\frac{3x}{10\times 100}\right)+2400x\left(-\frac{x}{4\times 100}\right)+40000\left(-\frac{x}{4\times 100}\right)+100000\left(-\frac{3x}{10\times 100}\right)+4400x-140000\left(-\frac{5x}{18\times 100}\right)-4400x\right)-440000x\left(-\frac{5x}{18\times 100}\right)=0$$

Multiply 40000 and -1 to get -40000. Multiply 100000 and -1 to get -100000. Multiply -1 and 140000 to get -140000.

$$100\left(2000x\left(-1\right)\times \frac{3x}{10\times 100}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 2000 and -1 to get -2000.

$$100\left(-2000x\times \frac{3x}{10\times 100}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 10 and 100 to get 1000.

$$100\left(-2000x\times \frac{3x}{1000}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Cancel out 1000, the greatest common factor in 2000 and 1000.

$$100\left(-2\times 3xx+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 2400 and -1 to get -2400.

$$100\left(-2\times 3xx-2400x\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 4 and 100 to get 400.

$$100\left(-2\times 3xx-2400x\times \frac{x}{400}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Cancel out 400, the greatest common factor in 2400 and 400.

$$100\left(-2\times 3xx-6xx-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 4 and 100 to get 400.

$$100\left(-2\times 3xx-6xx-40000\times \frac{x}{400}-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Cancel out 400, the greatest common factor in 40000 and 400.

$$100\left(-2\times 3xx-6xx-100x-100000\times \frac{3x}{10\times 100}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 10 and 100 to get 1000.

$$100\left(-2\times 3xx-6xx-100x-100000\times \frac{3x}{1000}+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Cancel out 1000, the greatest common factor in 100000 and 1000.

$$100\left(-2\times 3xx-6xx-100x-100\times 3x+4400x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Combine -100x and 4400x to get 4300x.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply -140000 and -1 to get 140000.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Cancel out 5 in both numerator and denominator.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000\times \frac{x}{18\times 20}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 18 and 20 to get 360.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000\times \frac{x}{360}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Express 140000\times \frac{x}{360} as a single fraction.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+\frac{140000x}{360}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Combine 4300x and -4400x to get -100x.

$$100\left(-2\times 3xx-6xx-100x-100\times 3x+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply -2 and 3 to get -6. Multiply -100 and 3 to get -300.

$$100\left(-6xx-6xx-100x-300x+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Combine -6xx and -6xx to get -12xx.

$$100\left(-12xx-100x-300x+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Combine -100x and -300x to get -400x.

$$100\left(-12xx-400x+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Use the distributive property to multiply 100 by -12xx-400x+\frac{140000x}{360}.

$$-1200x^{2}-40000x+100\times \frac{140000x}{360}-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Divide 140000x by 360 to get \frac{3500}{9}x.

$$-1200x^{2}-40000x+100\times \frac{3500}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Express 100\times \frac{3500}{9} as a single fraction.

$$-1200x^{2}-40000x+\frac{100\times 3500}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply 100 and 3500 to get 350000.

$$-1200x^{2}-40000x+\frac{350000}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Combine -40000x and \frac{350000}{9}x to get -\frac{10000}{9}x.

$$-1200x^{2}-\frac{10000}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=0$$

Multiply -440000 and -1 to get 440000.

$$-1200x^{2}-\frac{10000}{9}x+440000x\times \frac{5x}{18\times 100}=0$$

Cancel out 5 in both numerator and denominator.

$$-1200x^{2}-\frac{10000}{9}x+440000x\times \frac{x}{18\times 20}=0$$

Multiply 18 and 20 to get 360.

$$-1200x^{2}-\frac{10000}{9}x+440000x\times \frac{x}{360}=0$$

Express 440000\times \frac{x}{360} as a single fraction.

$$-1200x^{2}-\frac{10000}{9}x+\frac{440000x}{360}x=0$$

Divide 440000x by 360 to get \frac{11000}{9}x.

$$-1200x^{2}-\frac{10000}{9}x+\frac{11000}{9}xx=0$$

Multiply x and x to get x^{2}.

$$-1200x^{2}-\frac{10000}{9}x+\frac{11000}{9}x^{2}=0$$

Combine -1200x^{2} and \frac{11000}{9}x^{2} to get \frac{200}{9}x^{2}.

$$\frac{200}{9}x^{2}-\frac{10000}{9}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{200}{9} for a, -\frac{10000}{9} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{10000}{9}\right)±\sqrt{\left(-\frac{10000}{9}\right)^{2}}}{2\times \frac{200}{9}}$$

Take the square root of \left(-\frac{10000}{9}\right)^{2}.

$$x=\frac{-\left(-\frac{10000}{9}\right)±\frac{10000}{9}}{2\times \frac{200}{9}}$$

The opposite of -\frac{10000}{9} is \frac{10000}{9}.

$$x=\frac{\frac{10000}{9}±\frac{10000}{9}}{2\times \frac{200}{9}}$$

Multiply 2 times \frac{200}{9}.

$$x=\frac{\frac{10000}{9}±\frac{10000}{9}}{\frac{400}{9}}$$

Now solve the equation x=\frac{\frac{10000}{9}±\frac{10000}{9}}{\frac{400}{9}} when ± is plus. Add \frac{10000}{9} to \frac{10000}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{20000}{9}}{\frac{400}{9}}$$

Divide \frac{20000}{9} by \frac{400}{9} by multiplying \frac{20000}{9} by the reciprocal of \frac{400}{9}.

$$x=50$$

Now solve the equation x=\frac{\frac{10000}{9}±\frac{10000}{9}}{\frac{400}{9}} when ± is minus. Subtract \frac{10000}{9} from \frac{10000}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{\frac{400}{9}}$$

Divide 0 by \frac{400}{9} by multiplying 0 by the reciprocal of \frac{400}{9}.

$$x=0$$

The equation is now solved.

$$x=50 x=0$$

Steps for Completing the Square

Multiply both sides of the equation by 100.

$$2000\left(1+\frac{2x}{100}\right)\times 2.5\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 2x by 100 to get \frac{1}{50}x.

$$2000\left(1+\frac{1}{50}x\right)\times 2.5\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 2.5 to get 5000.

$$5000\left(1+\frac{1}{50}x\right)\times 20\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 5000 and 20 to get 100000.

$$100000\left(1+\frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 100000 by 1+\frac{1}{50}x.

$$\left(100000+100000\times \frac{1}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 100000 and \frac{1}{50} to get \frac{100000}{50}.

$$\left(100000+\frac{100000}{50}x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 100000 by 50 to get 2000.

$$\left(100000+2000x\right)\left(1-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 100000+2000x by each term of 1-\frac{\frac{3x}{10}}{100}.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{6x}{100}\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 6x by 100 to get \frac{3}{50}x.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+500\left(1+\frac{3}{50}x\right)\times 4\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 500 and 4 to get 2000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+2000\left(1+\frac{3}{50}x\right)\times 20\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 20 to get 40000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(1+\frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 40000 by 1+\frac{3}{50}x.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+40000\times \frac{3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 40000\times \frac{3}{50} as a single fraction.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{40000\times 3}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 40000 and 3 to get 120000.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+\frac{120000}{50}x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 120000 by 50 to get 2400.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+\left(40000+2400x\right)\left(1-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 40000+2400x by each term of 1-\frac{\frac{x}{4}}{100}.

$$100000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Add 100000 and 40000 to get 140000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+2000x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Combine 2000x and 2400x to get 4400x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{2x}{100}\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 2x by 100 to get \frac{1}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(20\left(1+\frac{1}{50}x\right)\times 2.5+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 20 and 2.5 to get 50.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50\left(1+\frac{1}{50}x\right)+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 50 by 1+\frac{1}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+50\times \frac{1}{50}x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Cancel out 50 and 50.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+5\left(1+\frac{6x}{100}\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 6x by 100 to get \frac{3}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+5\left(1+\frac{3}{50}x\right)\times 4\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 5 and 4 to get 20.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20\left(1+\frac{3}{50}x\right)\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 20 by 1+\frac{3}{50}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+20\times \frac{3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 20\times \frac{3}{50} as a single fraction.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{20\times 3}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 20 and 3 to get 60.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{60}{50}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Reduce the fraction \frac{60}{50} to lowest terms by extracting and canceling out 10.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(50+x+20+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Add 50 and 20 to get 70.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(70+x+\frac{6}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Combine x and \frac{6}{5}x to get \frac{11}{5}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=100\left(70+\frac{11}{5}x\right)\times 20\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 100 and 20 to get 2000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=2000\left(70+\frac{11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Use the distributive property to multiply 2000 by 70+\frac{11}{5}x.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+2000\times \frac{11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Express 2000\times \frac{11}{5} as a single fraction.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+\frac{2000\times 11}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Multiply 2000 and 11 to get 22000.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+\frac{22000}{5}x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Divide 22000 by 5 to get 4400.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=\left(140000+4400x\right)\left(1-\frac{\frac{5x}{18}}{100}\right)$$

Apply the distributive property by multiplying each term of 140000+4400x by each term of 1-\frac{\frac{5x}{18}}{100}.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)=140000+140000\left(-\frac{\frac{5x}{18}}{100}\right)+4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 140000\left(-\frac{\frac{5x}{18}}{100}\right) from both sides.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)=140000+4400x+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 4400x from both sides.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x=140000+4400x\left(-\frac{\frac{5x}{18}}{100}\right)$$

Subtract 4400x\left(-\frac{\frac{5x}{18}}{100}\right) from both sides.

$$140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x-4400x\left(-\frac{\frac{5x}{18}}{100}\right)=140000$$

Multiply both sides of the equation by 100.

$$100\left(140000+100000\left(-\frac{\frac{3x}{10}}{100}\right)+4400x+2000x\left(-\frac{\frac{3x}{10}}{100}\right)+40000\left(-\frac{\frac{x}{4}}{100}\right)+2400x\left(-\frac{\frac{x}{4}}{100}\right)-140000\left(-\frac{\frac{5x}{18}}{100}\right)-4400x\right)-440000x\left(-\frac{\frac{5x}{18}}{100}\right)=14000000$$

Reorder the terms.

$$100\left(2000x\left(-\frac{3x}{10\times 100}\right)+2400x\left(-\frac{x}{4\times 100}\right)+40000\left(-\frac{x}{4\times 100}\right)+100000\left(-\frac{3x}{10\times 100}\right)+4400x+140000-140000\left(-\frac{5x}{18\times 100}\right)-4400x\right)-440000x\left(-\frac{5x}{18\times 100}\right)=14000000$$

Multiply 40000 and -1 to get -40000. Multiply 100000 and -1 to get -100000. Multiply -1 and 140000 to get -140000.

$$100\left(2000x\left(-1\right)\times \frac{3x}{10\times 100}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 2000 and -1 to get -2000.

$$100\left(-2000x\times \frac{3x}{10\times 100}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 10 and 100 to get 1000.

$$100\left(-2000x\times \frac{3x}{1000}+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Cancel out 1000, the greatest common factor in 2000 and 1000.

$$100\left(-2\times 3xx+2400x\left(-1\right)\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 2400 and -1 to get -2400.

$$100\left(-2\times 3xx-2400x\times \frac{x}{4\times 100}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 4 and 100 to get 400.

$$100\left(-2\times 3xx-2400x\times \frac{x}{400}-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Cancel out 400, the greatest common factor in 2400 and 400.

$$100\left(-2\times 3xx-6xx-40000\times \frac{x}{4\times 100}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 4 and 100 to get 400.

$$100\left(-2\times 3xx-6xx-40000\times \frac{x}{400}-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Cancel out 400, the greatest common factor in 40000 and 400.

$$100\left(-2\times 3xx-6xx-100x-100000\times \frac{3x}{10\times 100}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 10 and 100 to get 1000.

$$100\left(-2\times 3xx-6xx-100x-100000\times \frac{3x}{1000}+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Cancel out 1000, the greatest common factor in 100000 and 1000.

$$100\left(-2\times 3xx-6xx-100x-100\times 3x+4400x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Combine -100x and 4400x to get 4300x.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000-140000\left(-1\right)\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply -140000 and -1 to get 140000.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000+140000\times \frac{5x}{18\times 100}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Cancel out 5 in both numerator and denominator.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000+140000\times \frac{x}{18\times 20}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 18 and 20 to get 360.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000+140000\times \frac{x}{360}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Express 140000\times \frac{x}{360} as a single fraction.

$$100\left(-2\times 3xx-6xx+4300x-100\times 3x+140000+\frac{140000x}{360}-4400x\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Combine 4300x and -4400x to get -100x.

$$100\left(-2\times 3xx-6xx-100x-100\times 3x+140000+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply -2 and 3 to get -6. Multiply -100 and 3 to get -300.

$$100\left(-6xx-6xx-100x-300x+140000+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Combine -6xx and -6xx to get -12xx.

$$100\left(-12xx-100x-300x+140000+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Combine -100x and -300x to get -400x.

$$100\left(-12xx-400x+140000+\frac{140000x}{360}\right)-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Use the distributive property to multiply 100 by -12xx-400x+140000+\frac{140000x}{360}.

$$-1200x^{2}-40000x+14000000+100\times \frac{140000x}{360}-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Divide 140000x by 360 to get \frac{3500}{9}x.

$$-1200x^{2}-40000x+14000000+100\times \frac{3500}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Express 100\times \frac{3500}{9} as a single fraction.

$$-1200x^{2}-40000x+14000000+\frac{100\times 3500}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply 100 and 3500 to get 350000.

$$-1200x^{2}-40000x+14000000+\frac{350000}{9}x-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Combine -40000x and \frac{350000}{9}x to get -\frac{10000}{9}x.

$$-1200x^{2}-\frac{10000}{9}x+14000000-440000x\left(-1\right)\times \frac{5x}{18\times 100}=14000000$$

Multiply -440000 and -1 to get 440000.

$$-1200x^{2}-\frac{10000}{9}x+14000000+440000x\times \frac{5x}{18\times 100}=14000000$$

Cancel out 5 in both numerator and denominator.

$$-1200x^{2}-\frac{10000}{9}x+14000000+440000x\times \frac{x}{18\times 20}=14000000$$

Multiply 18 and 20 to get 360.

$$-1200x^{2}-\frac{10000}{9}x+14000000+440000x\times \frac{x}{360}=14000000$$

Express 440000\times \frac{x}{360} as a single fraction.

$$-1200x^{2}-\frac{10000}{9}x+14000000+\frac{440000x}{360}x=14000000$$

Divide 440000x by 360 to get \frac{11000}{9}x.

$$-1200x^{2}-\frac{10000}{9}x+14000000+\frac{11000}{9}xx=14000000$$

Multiply x and x to get x^{2}.

$$-1200x^{2}-\frac{10000}{9}x+14000000+\frac{11000}{9}x^{2}=14000000$$

Combine -1200x^{2} and \frac{11000}{9}x^{2} to get \frac{200}{9}x^{2}.

$$\frac{200}{9}x^{2}-\frac{10000}{9}x+14000000=14000000$$

Subtract 14000000 from both sides.

$$\frac{200}{9}x^{2}-\frac{10000}{9}x=14000000-14000000$$

Subtract 14000000 from 14000000 to get 0.

$$\frac{200}{9}x^{2}-\frac{10000}{9}x=0$$

Divide both sides of the equation by \frac{200}{9}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{200}{9}x^{2}-\frac{10000}{9}x}{\frac{200}{9}}=\frac{0}{\frac{200}{9}}$$

Dividing by \frac{200}{9} undoes the multiplication by \frac{200}{9}.

$$x^{2}+\left(-\frac{\frac{10000}{9}}{\frac{200}{9}}\right)x=\frac{0}{\frac{200}{9}}$$

Divide -\frac{10000}{9} by \frac{200}{9} by multiplying -\frac{10000}{9} by the reciprocal of \frac{200}{9}.

$$x^{2}-50x=\frac{0}{\frac{200}{9}}$$

Divide 0 by \frac{200}{9} by multiplying 0 by the reciprocal of \frac{200}{9}.

$$x^{2}-50x=0$$

Divide -50, the coefficient of the x term, by 2 to get -25. Then add the square of -25 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-50x+\left(-25\right)^{2}=\left(-25\right)^{2}$$

Square -25.

$$x^{2}-50x+625=625$$

Factor x^{2}-50x+625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-25\right)^{2}=625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{625}$$

Simplify.

$$x-25=25 x-25=-25$$

Add 25 to both sides of the equation.

$$x=50 x=0$$