Issolvi 04+20/10=120/x+120/x+10

$$04 + \frac { 20 } { 10 } = \frac { 120 } { x } + \frac { 120 } { x + 10 }$$

Solvi għal x

$$x=5\sqrt{145}+55\approx 115.207972894$$

$$x=55-5\sqrt{145}\approx -5.207972894$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -10,0 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'10x\left(x+10\right), l-inqas denominatur komuni ta' 10,x,x+10.

$$0\times 4\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Immultiplika 0 u 4 biex tikseb 0.

$$0\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Immultiplika 0 u 10 biex tikseb 0.

$$0x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Xi ħaġa mmultiplikata b'żero jirriżulta f'żero.

$$0+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika x b'x+10.

$$0+\left(x^{2}+10x\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+10x b'20.

$$0+20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika 10x+100 b'120.

$$20x^{2}+200x=1200x+12000+10x\times 120$$

Immultiplika 10 u 120 biex tikseb 1200.

$$20x^{2}+200x=1200x+12000+1200x$$

Ikkombina 1200x u 1200x biex tikseb 2400x.

$$20x^{2}+200x=2400x+12000$$

Naqqas 2400x miż-żewġ naħat.

$$20x^{2}+200x-2400x=12000$$

Ikkombina 200x u -2400x biex tikseb -2200x.

$$20x^{2}-2200x=12000$$

Naqqas 12000 miż-żewġ naħat.

$$20x^{2}-2200x-12000=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 20 għal a, -2200 għal b, u -12000 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2200\right)±\sqrt{\left(-2200\right)^{2}-4\times 20\left(-12000\right)}}{2\times 20}$$

Ikkwadra -2200.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000-4\times 20\left(-12000\right)}}{2\times 20}$$

Immultiplika -4 b'20.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000-80\left(-12000\right)}}{2\times 20}$$

Immultiplika -80 b'-12000.

$$x=\frac{-\left(-2200\right)±\sqrt{4840000+960000}}{2\times 20}$$

Żid 4840000 ma' 960000.

$$x=\frac{-\left(-2200\right)±\sqrt{5800000}}{2\times 20}$$

Ħu l-għerq kwadrat ta' 5800000.

$$x=\frac{-\left(-2200\right)±200\sqrt{145}}{2\times 20}$$

L-oppost ta' -2200 huwa 2200.

$$x=\frac{2200±200\sqrt{145}}{2\times 20}$$

Immultiplika 2 b'20.

$$x=\frac{2200±200\sqrt{145}}{40}$$

Issa solvi l-ekwazzjoni x=\frac{2200±200\sqrt{145}}{40} fejn ± hija plus. Żid 2200 ma' 200\sqrt{145}.

$$x=\frac{200\sqrt{145}+2200}{40}$$

Iddividi 2200+200\sqrt{145} b'40.

$$x=5\sqrt{145}+55$$

Issa solvi l-ekwazzjoni x=\frac{2200±200\sqrt{145}}{40} fejn ± hija minus. Naqqas 200\sqrt{145} minn 2200.

$$x=\frac{2200-200\sqrt{145}}{40}$$

Iddividi 2200-200\sqrt{145} b'40.

$$x=55-5\sqrt{145}$$

L-ekwazzjoni issa solvuta.

$$x=5\sqrt{145}+55 x=55-5\sqrt{145}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -10,0 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'10x\left(x+10\right), l-inqas denominatur komuni ta' 10,x,x+10.

$$0\times 4\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Immultiplika 0 u 4 biex tikseb 0.

$$0\times 10x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Immultiplika 0 u 10 biex tikseb 0.

$$0x\left(x+10\right)+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Xi ħaġa mmultiplikata b'żero jirriżulta f'żero.

$$0+x\left(x+10\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika x b'x+10.

$$0+\left(x^{2}+10x\right)\times 20=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+10x b'20.

$$0+20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$20x^{2}+200x=\left(10x+100\right)\times 120+10x\times 120$$

Uża l-propjetà distributtiva biex timmultiplika 10x+100 b'120.

$$20x^{2}+200x=1200x+12000+10x\times 120$$

Immultiplika 10 u 120 biex tikseb 1200.

$$20x^{2}+200x=1200x+12000+1200x$$

Ikkombina 1200x u 1200x biex tikseb 2400x.

$$20x^{2}+200x=2400x+12000$$

Naqqas 2400x miż-żewġ naħat.

$$20x^{2}+200x-2400x=12000$$

Ikkombina 200x u -2400x biex tikseb -2200x.

$$20x^{2}-2200x=12000$$

Iddividi ż-żewġ naħat b'20.

$$\frac{20x^{2}-2200x}{20}=\frac{12000}{20}$$

Meta tiddividi b'20 titneħħa l-multiplikazzjoni b'20.

$$x^{2}+\left(-\frac{2200}{20}\right)x=\frac{12000}{20}$$

Iddividi -2200 b'20.

$$x^{2}-110x=\frac{12000}{20}$$

Iddividi 12000 b'20.

$$x^{2}-110x=600$$

Iddividi -110, il-koeffiċjent tat-terminu x, b'2 biex tikseb -55. Imbagħad żid il-kwadru ta' -55 maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-110x+\left(-55\right)^{2}=600+\left(-55\right)^{2}$$

Ikkwadra -55.

$$x^{2}-110x+3025=600+3025$$

Żid 600 ma' 3025.

$$x^{2}-110x+3025=3625$$

Fattur x^{2}-110x+3025. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-55\right)^{2}=3625$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x-55\right)^{2}}=\sqrt{3625}$$

Issimplifika.

$$x-55=5\sqrt{145} x-55=-5\sqrt{145}$$

Żid 55 maż-żewġ naħat tal-ekwazzjoni.

$$x=5\sqrt{145}+55 x=55-5\sqrt{145}$$