Issolvi x^2(6%)^2+(1-x)^2(2%)^2+2x(1-x)*012*6%*2%=00327

$$x ^ { 2 } ( 6 \% ) ^ { 2 } + ( 1 - x ) ^ { 2 } ( 2 \% ) ^ { 2 } + 2 x ( 1 - x ) \times 012 \times 6 \% \times 2 \% = 00327$$

Solvi għal x (complex solution)

$$x=\frac{1}{10}+\frac{3}{10}i=0.1+0.3i$$

$$x=\frac{1}{10}-\frac{3}{10}i=0.1-0.3i$$

Passi għall-Użu tal-Formula Kwadratika

Naqqas il-frazzjoni \frac{6}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x^{2}\times \left(\frac{3}{50}\right)^{2}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkalkula \frac{3}{50} bil-power ta' 2 u tikseb \frac{9}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-x\right)^{2}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{2}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{1}{50}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkalkula \frac{1}{50} bil-power ta' 2 u tikseb \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \frac{1}{2500}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Uża l-propjetà distributtiva biex timmultiplika 1-2x+x^{2} b'\frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\frac{1}{2500}-\frac{1}{1250}x+\frac{1}{2500}x^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkombina x^{2}\times \frac{9}{2500} u \frac{1}{2500}x^{2} biex tikseb \frac{1}{250}x^{2}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 2 u 0 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 0 u 12 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{6}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{3}{50}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 0 u \frac{3}{50} biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{2}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{1}{50}=0\times 0\times 327$$

Immultiplika 0 u \frac{1}{50} biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)=0\times 0\times 327$$

Xi ħaġa mmultiplikata b'żero jirriżulta f'żero.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0=0\times 0\times 327$$

Żid \frac{1}{2500} u 0 biex tikseb \frac{1}{2500}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 0\times 327$$

Immultiplika 0 u 0 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 327$$

Immultiplika 0 u 327 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0$$

L-ekwazzjonijiet kollha tal-formola ax^{2}+bx+c=0 jistgħu jiġu solvuti permezz tal-formula kwadratika: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Il-formula kwadratika tagħti żewġ soluzzjonijiet, waħda meta ± hija addizzjoni u waħda meta hija tnaqqis.

$$\frac{1}{250}x^{2}-\frac{1}{1250}x+\frac{1}{2500}=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi \frac{1}{250} għal a, -\frac{1}{1250} għal b, u \frac{1}{2500} għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\left(-\frac{1}{1250}\right)^{2}-4\times \frac{1}{250}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Ikkwadra -\frac{1}{1250} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-4\times \frac{1}{250}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Immultiplika -4 b'\frac{1}{250}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-\frac{2}{125}\times \frac{1}{2500}}}{2\times \frac{1}{250}}$$

Immultiplika -\frac{2}{125} b'\frac{1}{2500} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur. Imbagħad naqqas il-frazzjoni għall-inqas termini jekk possibbli.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{\frac{1}{1562500}-\frac{1}{156250}}}{2\times \frac{1}{250}}$$

Żid \frac{1}{1562500} ma' -\frac{1}{156250} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\sqrt{-\frac{9}{1562500}}}{2\times \frac{1}{250}}$$

Ħu l-għerq kwadrat ta' -\frac{9}{1562500}.

$$x=\frac{-\left(-\frac{1}{1250}\right)±\frac{3}{1250}i}{2\times \frac{1}{250}}$$

L-oppost ta' -\frac{1}{1250} huwa \frac{1}{1250}.

$$x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{2\times \frac{1}{250}}$$

Immultiplika 2 b'\frac{1}{250}.

$$x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}} fejn ± hija plus. Żid \frac{1}{1250} ma' \frac{3}{1250}i.

$$x=\frac{\frac{1}{1250}+\frac{3}{1250}i}{\frac{1}{125}}$$

Iddividi \frac{1}{1250}+\frac{3}{1250}i b'\frac{1}{125} billi timmultiplika \frac{1}{1250}+\frac{3}{1250}i bir-reċiproku ta' \frac{1}{125}.

$$x=\frac{1}{10}+\frac{3}{10}i$$

Issa solvi l-ekwazzjoni x=\frac{\frac{1}{1250}±\frac{3}{1250}i}{\frac{1}{125}} fejn ± hija minus. Naqqas \frac{3}{1250}i minn \frac{1}{1250}.

$$x=\frac{\frac{1}{1250}-\frac{3}{1250}i}{\frac{1}{125}}$$

Iddividi \frac{1}{1250}-\frac{3}{1250}i b'\frac{1}{125} billi timmultiplika \frac{1}{1250}-\frac{3}{1250}i bir-reċiproku ta' \frac{1}{125}.

$$x=\frac{1}{10}-\frac{3}{10}i$$

L-ekwazzjoni issa solvuta.

$$x=\frac{1}{10}+\frac{3}{10}i x=\frac{1}{10}-\frac{3}{10}i$$

Passi biex Tikkompleta l-Kwadrat

Naqqas il-frazzjoni \frac{6}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x^{2}\times \left(\frac{3}{50}\right)^{2}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkalkula \frac{3}{50} bil-power ta' 2 u tikseb \frac{9}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-x\right)^{2}\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(1-x\right)^{2}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{2}{100}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{2}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \left(\frac{1}{50}\right)^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkalkula \frac{1}{50} bil-power ta' 2 u tikseb \frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\left(1-2x+x^{2}\right)\times \frac{1}{2500}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Uża l-propjetà distributtiva biex timmultiplika 1-2x+x^{2} b'\frac{1}{2500}.

$$x^{2}\times \frac{9}{2500}+\frac{1}{2500}-\frac{1}{1250}x+\frac{1}{2500}x^{2}+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Ikkombina x^{2}\times \frac{9}{2500} u \frac{1}{2500}x^{2} biex tikseb \frac{1}{250}x^{2}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+2x\left(1-x\right)\times 0\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 2 u 0 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times 12\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 0 u 12 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{6}{100}\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{6}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{3}{50}\times \frac{2}{100}=0\times 0\times 327$$

Immultiplika 0 u \frac{3}{50} biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{2}{100}=0\times 0\times 327$$

Naqqas il-frazzjoni \frac{2}{100} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)\times \frac{1}{50}=0\times 0\times 327$$

Immultiplika 0 u \frac{1}{50} biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0x\left(1-x\right)=0\times 0\times 327$$

Xi ħaġa mmultiplikata b'żero jirriżulta f'żero.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x+0=0\times 0\times 327$$

Żid \frac{1}{2500} u 0 biex tikseb \frac{1}{2500}.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 0\times 327$$

Immultiplika 0 u 0 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0\times 327$$

Immultiplika 0 u 327 biex tikseb 0.

$$\frac{1}{250}x^{2}+\frac{1}{2500}-\frac{1}{1250}x=0$$

Naqqas \frac{1}{2500} miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$\frac{1}{250}x^{2}-\frac{1}{1250}x=-\frac{1}{2500}$$

Immultiplika ż-żewġ naħat b'250.

$$\frac{\frac{1}{250}x^{2}-\frac{1}{1250}x}{\frac{1}{250}}=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Meta tiddividi b'\frac{1}{250} titneħħa l-multiplikazzjoni b'\frac{1}{250}.

$$x^{2}+\left(-\frac{\frac{1}{1250}}{\frac{1}{250}}\right)x=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Iddividi -\frac{1}{1250} b'\frac{1}{250} billi timmultiplika -\frac{1}{1250} bir-reċiproku ta' \frac{1}{250}.

$$x^{2}-\frac{1}{5}x=-\frac{\frac{1}{2500}}{\frac{1}{250}}$$

Iddividi -\frac{1}{2500} b'\frac{1}{250} billi timmultiplika -\frac{1}{2500} bir-reċiproku ta' \frac{1}{250}.

$$x^{2}-\frac{1}{5}x=-\frac{1}{10}$$

Iddividi -\frac{1}{5}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{1}{10}. Imbagħad żid il-kwadru ta' -\frac{1}{10} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{1}{5}x+\left(-\frac{1}{10}\right)^{2}=-\frac{1}{10}+\left(-\frac{1}{10}\right)^{2}$$

Ikkwadra -\frac{1}{10} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=-\frac{1}{10}+\frac{1}{100}$$

Żid -\frac{1}{10} ma' \frac{1}{100} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=-\frac{9}{100}$$

Fattur x^{2}-\frac{1}{5}x+\frac{1}{100}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{10}\right)^{2}=-\frac{9}{100}$$

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

$$\sqrt{\left(x-\frac{1}{10}\right)^{2}}=\sqrt{-\frac{9}{100}}$$

Issimplifika.

$$x-\frac{1}{10}=\frac{3}{10}i x-\frac{1}{10}=-\frac{3}{10}i$$

Żid \frac{1}{10} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{1}{10}+\frac{3}{10}i x=\frac{1}{10}-\frac{3}{10}i$$