Issolvi 1/5x-3=5x(1/10x+1/10)

$$\frac { 1 } { 5 } x - 3 = 5 x ( \frac { 1 } { 10 } x + \frac { 1 } { 10 } )$$

Solvi għal x (complex solution)

$$x=\frac{-3+\sqrt{591}i}{10}\approx -0.3+2.431049156i$$

$$x=\frac{-\sqrt{591}i-3}{10}\approx -0.3-2.431049156i$$

Passi għall-Użu tal-Formula Kwadratika

Uża l-propjetà distributtiva biex timmultiplika 5x b'\frac{1}{10}x+\frac{1}{10}.

$$\frac{1}{5}x-3=5x\times \frac{1}{10}x+5x\times \frac{1}{10}$$

Immultiplika x u x biex tikseb x^{2}.

$$\frac{1}{5}x-3=5x^{2}\times \frac{1}{10}+5x\times \frac{1}{10}$$

Immultiplika 5 u \frac{1}{10} biex tikseb \frac{5}{10}.

$$\frac{1}{5}x-3=\frac{5}{10}x^{2}+5x\times \frac{1}{10}$$

Naqqas il-frazzjoni \frac{5}{10} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+5x\times \frac{1}{10}$$

Immultiplika 5 u \frac{1}{10} biex tikseb \frac{5}{10}.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+\frac{5}{10}x$$

Naqqas il-frazzjoni \frac{5}{10} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+\frac{1}{2}x$$

Naqqas \frac{1}{2}x^{2} miż-żewġ naħat.

$$\frac{1}{5}x-3-\frac{1}{2}x^{2}=\frac{1}{2}x$$

Naqqas \frac{1}{2}x miż-żewġ naħat.

$$\frac{1}{5}x-3-\frac{1}{2}x^{2}-\frac{1}{2}x=0$$

Ikkombina \frac{1}{5}x u -\frac{1}{2}x biex tikseb -\frac{3}{10}x.

$$-\frac{3}{10}x-3-\frac{1}{2}x^{2}=0$$

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.

$$-\frac{1}{2}x^{2}-\frac{3}{10}x-3=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -\frac{1}{2} għal a, -\frac{3}{10} għal b, u -3 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{3}{10}\right)±\sqrt{\left(-\frac{3}{10}\right)^{2}-4\left(-\frac{1}{2}\right)\left(-3\right)}}{2\left(-\frac{1}{2}\right)}$$

Ikkwadra -\frac{3}{10} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x=\frac{-\left(-\frac{3}{10}\right)±\sqrt{\frac{9}{100}-4\left(-\frac{1}{2}\right)\left(-3\right)}}{2\left(-\frac{1}{2}\right)}$$

Immultiplika -4 b'-\frac{1}{2}.

$$x=\frac{-\left(-\frac{3}{10}\right)±\sqrt{\frac{9}{100}+2\left(-3\right)}}{2\left(-\frac{1}{2}\right)}$$

Immultiplika 2 b'-3.

$$x=\frac{-\left(-\frac{3}{10}\right)±\sqrt{\frac{9}{100}-6}}{2\left(-\frac{1}{2}\right)}$$

Żid \frac{9}{100} ma' -6.

$$x=\frac{-\left(-\frac{3}{10}\right)±\sqrt{-\frac{591}{100}}}{2\left(-\frac{1}{2}\right)}$$

Ħu l-għerq kwadrat ta' -\frac{591}{100}.

$$x=\frac{-\left(-\frac{3}{10}\right)±\frac{\sqrt{591}i}{10}}{2\left(-\frac{1}{2}\right)}$$

L-oppost ta' -\frac{3}{10} huwa \frac{3}{10}.

$$x=\frac{\frac{3}{10}±\frac{\sqrt{591}i}{10}}{2\left(-\frac{1}{2}\right)}$$

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

$$x=\frac{\frac{3}{10}±\frac{\sqrt{591}i}{10}}{-1}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{3}{10}±\frac{\sqrt{591}i}{10}}{-1} fejn ± hija plus. Żid \frac{3}{10} ma' \frac{i\sqrt{591}}{10}.

$$x=\frac{3+\sqrt{591}i}{-10}$$

Iddividi \frac{3+i\sqrt{591}}{10} b'-1.

$$x=\frac{-\sqrt{591}i-3}{10}$$

Issa solvi l-ekwazzjoni x=\frac{\frac{3}{10}±\frac{\sqrt{591}i}{10}}{-1} fejn ± hija minus. Naqqas \frac{i\sqrt{591}}{10} minn \frac{3}{10}.

$$x=\frac{-\sqrt{591}i+3}{-10}$$

Iddividi \frac{3-i\sqrt{591}}{10} b'-1.

$$x=\frac{-3+\sqrt{591}i}{10}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{-\sqrt{591}i-3}{10} x=\frac{-3+\sqrt{591}i}{10}$$

Passi biex Tikkompleta l-Kwadrat

Uża l-propjetà distributtiva biex timmultiplika 5x b'\frac{1}{10}x+\frac{1}{10}.

$$\frac{1}{5}x-3=5x\times \frac{1}{10}x+5x\times \frac{1}{10}$$

Immultiplika x u x biex tikseb x^{2}.

$$\frac{1}{5}x-3=5x^{2}\times \frac{1}{10}+5x\times \frac{1}{10}$$

Immultiplika 5 u \frac{1}{10} biex tikseb \frac{5}{10}.

$$\frac{1}{5}x-3=\frac{5}{10}x^{2}+5x\times \frac{1}{10}$$

Naqqas il-frazzjoni \frac{5}{10} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+5x\times \frac{1}{10}$$

Immultiplika 5 u \frac{1}{10} biex tikseb \frac{5}{10}.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+\frac{5}{10}x$$

Naqqas il-frazzjoni \frac{5}{10} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

$$\frac{1}{5}x-3=\frac{1}{2}x^{2}+\frac{1}{2}x$$

Naqqas \frac{1}{2}x^{2} miż-żewġ naħat.

$$\frac{1}{5}x-3-\frac{1}{2}x^{2}=\frac{1}{2}x$$

Naqqas \frac{1}{2}x miż-żewġ naħat.

$$\frac{1}{5}x-3-\frac{1}{2}x^{2}-\frac{1}{2}x=0$$

Ikkombina \frac{1}{5}x u -\frac{1}{2}x biex tikseb -\frac{3}{10}x.

$$-\frac{3}{10}x-3-\frac{1}{2}x^{2}=0$$

Żid 3 maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$-\frac{3}{10}x-\frac{1}{2}x^{2}=3$$

Ekwazzjonijiet kwadratiċi bħal din jistgħu jiġu solvuti billi tikkompleta l-kwadrat. Sabiex tikkompleta l-kwadrat, l-ekwazzjoni l-ewwel trid tkun fil-forma x^{2}+bx=c.

$$-\frac{1}{2}x^{2}-\frac{3}{10}x=3$$

Immultiplika ż-żewġ naħat b'-2.

$$\frac{-\frac{1}{2}x^{2}-\frac{3}{10}x}{-\frac{1}{2}}=\frac{3}{-\frac{1}{2}}$$

Meta tiddividi b'-\frac{1}{2} titneħħa l-multiplikazzjoni b'-\frac{1}{2}.

$$x^{2}+\left(-\frac{\frac{3}{10}}{-\frac{1}{2}}\right)x=\frac{3}{-\frac{1}{2}}$$

Iddividi -\frac{3}{10} b'-\frac{1}{2} billi timmultiplika -\frac{3}{10} bir-reċiproku ta' -\frac{1}{2}.

$$x^{2}+\frac{3}{5}x=\frac{3}{-\frac{1}{2}}$$

Iddividi 3 b'-\frac{1}{2} billi timmultiplika 3 bir-reċiproku ta' -\frac{1}{2}.

$$x^{2}+\frac{3}{5}x=-6$$

Iddividi \frac{3}{5}, il-koeffiċjent tat-terminu x, b'2 biex tikseb \frac{3}{10}. Imbagħad żid il-kwadru ta' \frac{3}{10} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+\frac{3}{5}x+\left(\frac{3}{10}\right)^{2}=-6+\left(\frac{3}{10}\right)^{2}$$

Ikkwadra \frac{3}{10} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}+\frac{3}{5}x+\frac{9}{100}=-6+\frac{9}{100}$$

Żid -6 ma' \frac{9}{100}.

$$x^{2}+\frac{3}{5}x+\frac{9}{100}=-\frac{591}{100}$$

Fattur x^{2}+\frac{3}{5}x+\frac{9}{100}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{10}\right)^{2}=-\frac{591}{100}$$

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

$$\sqrt{\left(x+\frac{3}{10}\right)^{2}}=\sqrt{-\frac{591}{100}}$$

Issimplifika.

$$x+\frac{3}{10}=\frac{\sqrt{591}i}{10} x+\frac{3}{10}=-\frac{\sqrt{591}i}{10}$$

Naqqas \frac{3}{10} miż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{-3+\sqrt{591}i}{10} x=\frac{-\sqrt{591}i-3}{10}$$