Issolvi (2x-40)(3x-50)*(30+100)+2000*1000=64000

$$( 2 x - 40 ) ( 3 x - 50 ) \times ( 30 + 100 ) + 2000 \times 1000 = 64000$$

Solvi għal x (complex solution)

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18.333333333+49.792303665i$$

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18.333333333-49.792303665i$$

Passi għall-Użu tal-Formula Kwadratika

Żid 30 u 100 biex tikseb 130.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

Uża l-propjetà distributtiva biex timmultiplika 2x-40 b'3x-50 u kkombina termini simili.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

Uża l-propjetà distributtiva biex timmultiplika 6x^{2}-220x+2000 b'130.

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

Immultiplika 2000 u 1000 biex tikseb 2000000.

$$780x^{2}-28600x+260000+2000000=64000$$

Żid 260000 u 2000000 biex tikseb 2260000.

$$780x^{2}-28600x+2260000=64000$$

Naqqas 64000 miż-żewġ naħat.

$$780x^{2}-28600x+2260000-64000=0$$

Naqqas 64000 minn 2260000 biex tikseb 2196000.

$$780x^{2}-28600x+2196000=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 780 għal a, -28600 għal b, u 2196000 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-28600\right)±\sqrt{\left(-28600\right)^{2}-4\times 780\times 2196000}}{2\times 780}$$

Ikkwadra -28600.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-4\times 780\times 2196000}}{2\times 780}$$

Immultiplika -4 b'780.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-3120\times 2196000}}{2\times 780}$$

Immultiplika -3120 b'2196000.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-6851520000}}{2\times 780}$$

Żid 817960000 ma' -6851520000.

$$x=\frac{-\left(-28600\right)±\sqrt{-6033560000}}{2\times 780}$$

Ħu l-għerq kwadrat ta' -6033560000.

$$x=\frac{-\left(-28600\right)±200\sqrt{150839}i}{2\times 780}$$

L-oppost ta' -28600 huwa 28600.

$$x=\frac{28600±200\sqrt{150839}i}{2\times 780}$$

Immultiplika 2 b'780.

$$x=\frac{28600±200\sqrt{150839}i}{1560}$$

Issa solvi l-ekwazzjoni x=\frac{28600±200\sqrt{150839}i}{1560} fejn ± hija plus. Żid 28600 ma' 200i\sqrt{150839}.

$$x=\frac{28600+200\sqrt{150839}i}{1560}$$

Iddividi 28600+200i\sqrt{150839} b'1560.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Issa solvi l-ekwazzjoni x=\frac{28600±200\sqrt{150839}i}{1560} fejn ± hija minus. Naqqas 200i\sqrt{150839} minn 28600.

$$x=\frac{-200\sqrt{150839}i+28600}{1560}$$

Iddividi 28600-200i\sqrt{150839} b'1560.

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Passi biex Tikkompleta l-Kwadrat

Żid 30 u 100 biex tikseb 130.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

Uża l-propjetà distributtiva biex timmultiplika 2x-40 b'3x-50 u kkombina termini simili.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

Uża l-propjetà distributtiva biex timmultiplika 6x^{2}-220x+2000 b'130.

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

Immultiplika 2000 u 1000 biex tikseb 2000000.

$$780x^{2}-28600x+260000+2000000=64000$$

Żid 260000 u 2000000 biex tikseb 2260000.

$$780x^{2}-28600x+2260000=64000$$

Naqqas 2260000 miż-żewġ naħat.

$$780x^{2}-28600x=64000-2260000$$

Naqqas 2260000 minn 64000 biex tikseb -2196000.

$$780x^{2}-28600x=-2196000$$

Iddividi ż-żewġ naħat b'780.

$$\frac{780x^{2}-28600x}{780}=-\frac{2196000}{780}$$

Meta tiddividi b'780 titneħħa l-multiplikazzjoni b'780.

$$x^{2}+\left(-\frac{28600}{780}\right)x=-\frac{2196000}{780}$$

Naqqas il-frazzjoni \frac{-28600}{780} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 260.

$$x^{2}-\frac{110}{3}x=-\frac{2196000}{780}$$

Naqqas il-frazzjoni \frac{-2196000}{780} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 60.

$$x^{2}-\frac{110}{3}x=-\frac{36600}{13}$$

Iddividi -\frac{110}{3}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{55}{3}. Imbagħad żid il-kwadru ta' -\frac{55}{3} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{110}{3}x+\left(-\frac{55}{3}\right)^{2}=-\frac{36600}{13}+\left(-\frac{55}{3}\right)^{2}$$

Ikkwadra -\frac{55}{3} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{36600}{13}+\frac{3025}{9}$$

Żid -\frac{36600}{13} ma' \frac{3025}{9} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{290075}{117}$$

Fattur x^{2}-\frac{110}{3}x+\frac{3025}{9}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{55}{3}\right)^{2}=-\frac{290075}{117}$$

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

$$\sqrt{\left(x-\frac{55}{3}\right)^{2}}=\sqrt{-\frac{290075}{117}}$$

Issimplifika.

$$x-\frac{55}{3}=\frac{5\sqrt{150839}i}{39} x-\frac{55}{3}=-\frac{5\sqrt{150839}i}{39}$$

Żid \frac{55}{3} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$