Issolvi (2x)^2/(1-x)(1-5-x)=12*10^-2

$$\frac { ( 2 x ) ^ { 2 } } { ( 1 - x ) ( 1 - 5 - x ) } = 12 \times 10 ^ { - 2 }$$

Solvi għal x (complex solution)

$$x=\frac{9+5\sqrt{183}i}{194}\approx 0.046391753+0.348653331i$$

$$x=\frac{-5\sqrt{183}i+9}{194}\approx 0.046391753-0.348653331i$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -4,1 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-1\right)\left(x+4\right).

$$\left(2x\right)^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Espandi \left(2x\right)^{2}.

$$2^{2}x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$4x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Ikkalkula 10 bil-power ta' -2 u tikseb \frac{1}{100}.

$$4x^{2}=12\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Immultiplika 12 u \frac{1}{100} biex tikseb \frac{3}{25}.

$$4x^{2}=\frac{3}{25}\left(x-1\right)\left(x+4\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{3}{25} b'x-1.

$$4x^{2}=\left(\frac{3}{25}x-\frac{3}{25}\right)\left(x+4\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{3}{25}x-\frac{3}{25} b'x+4 u kkombina termini simili.

$$4x^{2}=\frac{3}{25}x^{2}+\frac{9}{25}x-\frac{12}{25}$$

Naqqas \frac{3}{25}x^{2} miż-żewġ naħat.

$$4x^{2}-\frac{3}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Ikkombina 4x^{2} u -\frac{3}{25}x^{2} biex tikseb \frac{97}{25}x^{2}.

$$\frac{97}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Naqqas \frac{9}{25}x miż-żewġ naħat.

$$\frac{97}{25}x^{2}-\frac{9}{25}x=-\frac{12}{25}$$

Żid \frac{12}{25} maż-żewġ naħat.

$$\frac{97}{25}x^{2}-\frac{9}{25}x+\frac{12}{25}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi \frac{97}{25} għal a, -\frac{9}{25} għal b, u \frac{12}{25} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\left(-\frac{9}{25}\right)^{2}-4\times \frac{97}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Ikkwadra -\frac{9}{25} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81}{625}-4\times \frac{97}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Immultiplika -4 b'\frac{97}{25}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81}{625}-\frac{388}{25}\times \frac{12}{25}}}{2\times \frac{97}{25}}$$

Immultiplika -\frac{388}{25} b'\frac{12}{25} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur. Imbagħad naqqas il-frazzjoni għall-inqas termini jekk possibbli.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{\frac{81-4656}{625}}}{2\times \frac{97}{25}}$$

Żid \frac{81}{625} ma' -\frac{4656}{625} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\left(-\frac{9}{25}\right)±\sqrt{-\frac{183}{25}}}{2\times \frac{97}{25}}$$

Ħu l-għerq kwadrat ta' -\frac{183}{25}.

$$x=\frac{-\left(-\frac{9}{25}\right)±\frac{\sqrt{183}i}{5}}{2\times \frac{97}{25}}$$

L-oppost ta' -\frac{9}{25} huwa \frac{9}{25}.

$$x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{2\times \frac{97}{25}}$$

Immultiplika 2 b'\frac{97}{25}.

$$x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}} fejn ± hija plus. Żid \frac{9}{25} ma' \frac{i\sqrt{183}}{5}.

$$x=\frac{\frac{\sqrt{183}i}{5}+\frac{9}{25}}{\frac{194}{25}}$$

Iddividi \frac{9}{25}+\frac{i\sqrt{183}}{5} b'\frac{194}{25} billi timmultiplika \frac{9}{25}+\frac{i\sqrt{183}}{5} bir-reċiproku ta' \frac{194}{25}.

$$x=\frac{9+5\sqrt{183}i}{194}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{9}{25}±\frac{\sqrt{183}i}{5}}{\frac{194}{25}} fejn ± hija minus. Naqqas \frac{i\sqrt{183}}{5} minn \frac{9}{25}.

$$x=\frac{-\frac{\sqrt{183}i}{5}+\frac{9}{25}}{\frac{194}{25}}$$

Iddividi \frac{9}{25}-\frac{i\sqrt{183}}{5} b'\frac{194}{25} billi timmultiplika \frac{9}{25}-\frac{i\sqrt{183}}{5} bir-reċiproku ta' \frac{194}{25}.

$$x=\frac{-5\sqrt{183}i+9}{194}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{9+5\sqrt{183}i}{194} x=\frac{-5\sqrt{183}i+9}{194}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -4,1 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-1\right)\left(x+4\right).

$$\left(2x\right)^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Espandi \left(2x\right)^{2}.

$$2^{2}x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$4x^{2}=12\times 10^{-2}\left(x-1\right)\left(x+4\right)$$

Ikkalkula 10 bil-power ta' -2 u tikseb \frac{1}{100}.

$$4x^{2}=12\times \frac{1}{100}\left(x-1\right)\left(x+4\right)$$

Immultiplika 12 u \frac{1}{100} biex tikseb \frac{3}{25}.

$$4x^{2}=\frac{3}{25}\left(x-1\right)\left(x+4\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{3}{25} b'x-1.

$$4x^{2}=\left(\frac{3}{25}x-\frac{3}{25}\right)\left(x+4\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{3}{25}x-\frac{3}{25} b'x+4 u kkombina termini simili.

$$4x^{2}=\frac{3}{25}x^{2}+\frac{9}{25}x-\frac{12}{25}$$

Naqqas \frac{3}{25}x^{2} miż-żewġ naħat.

$$4x^{2}-\frac{3}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Ikkombina 4x^{2} u -\frac{3}{25}x^{2} biex tikseb \frac{97}{25}x^{2}.

$$\frac{97}{25}x^{2}=\frac{9}{25}x-\frac{12}{25}$$

Naqqas \frac{9}{25}x miż-żewġ naħat.

$$\frac{97}{25}x^{2}-\frac{9}{25}x=-\frac{12}{25}$$

Iddividi ż-żewġ naħat tal-ekwazzjoni b'\frac{97}{25}, li hija l-istess bħal multiplikazzjoni taż-żewġ naħat bir-reċiproku tal-frazzjoni.

$$\frac{\frac{97}{25}x^{2}-\frac{9}{25}x}{\frac{97}{25}}=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Meta tiddividi b'\frac{97}{25} titneħħa l-multiplikazzjoni b'\frac{97}{25}.

$$x^{2}+\left(-\frac{\frac{9}{25}}{\frac{97}{25}}\right)x=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Iddividi -\frac{9}{25} b'\frac{97}{25} billi timmultiplika -\frac{9}{25} bir-reċiproku ta' \frac{97}{25}.

$$x^{2}-\frac{9}{97}x=-\frac{\frac{12}{25}}{\frac{97}{25}}$$

Iddividi -\frac{12}{25} b'\frac{97}{25} billi timmultiplika -\frac{12}{25} bir-reċiproku ta' \frac{97}{25}.

$$x^{2}-\frac{9}{97}x=-\frac{12}{97}$$

Iddividi -\frac{9}{97}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{9}{194}. Imbagħad żid il-kwadru ta' -\frac{9}{194} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{9}{97}x+\left(-\frac{9}{194}\right)^{2}=-\frac{12}{97}+\left(-\frac{9}{194}\right)^{2}$$

Ikkwadra -\frac{9}{194} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{9}{97}x+\frac{81}{37636}=-\frac{12}{97}+\frac{81}{37636}$$

Żid -\frac{12}{97} ma' \frac{81}{37636} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{9}{97}x+\frac{81}{37636}=-\frac{4575}{37636}$$

Fattur x^{2}-\frac{9}{97}x+\frac{81}{37636}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{194}\right)^{2}=-\frac{4575}{37636}$$

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

$$\sqrt{\left(x-\frac{9}{194}\right)^{2}}=\sqrt{-\frac{4575}{37636}}$$

Issimplifika.

$$x-\frac{9}{194}=\frac{5\sqrt{183}i}{194} x-\frac{9}{194}=-\frac{5\sqrt{183}i}{194}$$

Żid \frac{9}{194} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{9+5\sqrt{183}i}{194} x=\frac{-5\sqrt{183}i+9}{194}$$