Issolvi (6v-9)(2v+1)=7v^2-38-33

$$( 6 v - 9 ) ( 2 v + 1 ) = 7 v ^ { 2 } - 38 - 33$$

Solvi għal v

$$v=\frac{6+\sqrt{274}i}{5}\approx 1.2+3.310589071i$$

$$v=\frac{-\sqrt{274}i+6}{5}\approx 1.2-3.310589071i$$

Passi għall-Użu tal-Formula Kwadratika

Uża l-propjetà distributtiva biex timmultiplika 6v-9 b'2v+1 u kkombina termini simili.

$$12v^{2}-12v-9=7v^{2}-38-33$$

Naqqas 33 minn -38 biex tikseb -71.

$$12v^{2}-12v-9=7v^{2}-71$$

Naqqas 7v^{2} miż-żewġ naħat.

$$12v^{2}-12v-9-7v^{2}=-71$$

Ikkombina 12v^{2} u -7v^{2} biex tikseb 5v^{2}.

$$5v^{2}-12v-9=-71$$

Żid 71 maż-żewġ naħat.

$$5v^{2}-12v-9+71=0$$

Żid -9 u 71 biex tikseb 62.

$$5v^{2}-12v+62=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 5 għal a, -12 għal b, u 62 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 5\times 62}}{2\times 5}$$

Ikkwadra -12.

$$v=\frac{-\left(-12\right)±\sqrt{144-4\times 5\times 62}}{2\times 5}$$

Immultiplika -4 b'5.

$$v=\frac{-\left(-12\right)±\sqrt{144-20\times 62}}{2\times 5}$$

Immultiplika -20 b'62.

$$v=\frac{-\left(-12\right)±\sqrt{144-1240}}{2\times 5}$$

Żid 144 ma' -1240.

$$v=\frac{-\left(-12\right)±\sqrt{-1096}}{2\times 5}$$

Ħu l-għerq kwadrat ta' -1096.

$$v=\frac{-\left(-12\right)±2\sqrt{274}i}{2\times 5}$$

L-oppost ta' -12 huwa 12.

$$v=\frac{12±2\sqrt{274}i}{2\times 5}$$

Immultiplika 2 b'5.

$$v=\frac{12±2\sqrt{274}i}{10}$$

Issa solvi l-ekwazzjoni v=\frac{12±2\sqrt{274}i}{10} fejn ± hija plus. Żid 12 ma' 2i\sqrt{274}.

$$v=\frac{12+2\sqrt{274}i}{10}$$

Iddividi 12+2i\sqrt{274} b'10.

$$v=\frac{6+\sqrt{274}i}{5}$$

Issa solvi l-ekwazzjoni v=\frac{12±2\sqrt{274}i}{10} fejn ± hija minus. Naqqas 2i\sqrt{274} minn 12.

$$v=\frac{-2\sqrt{274}i+12}{10}$$

Iddividi 12-2i\sqrt{274} b'10.

$$v=\frac{-\sqrt{274}i+6}{5}$$

L-ekwazzjoni issa solvuta.

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$

Passi biex Tikkompleta l-Kwadrat

Uża l-propjetà distributtiva biex timmultiplika 6v-9 b'2v+1 u kkombina termini simili.

$$12v^{2}-12v-9=7v^{2}-38-33$$

Naqqas 33 minn -38 biex tikseb -71.

$$12v^{2}-12v-9=7v^{2}-71$$

Naqqas 7v^{2} miż-żewġ naħat.

$$12v^{2}-12v-9-7v^{2}=-71$$

Ikkombina 12v^{2} u -7v^{2} biex tikseb 5v^{2}.

$$5v^{2}-12v-9=-71$$

Żid 9 maż-żewġ naħat.

$$5v^{2}-12v=-71+9$$

Żid -71 u 9 biex tikseb -62.

$$5v^{2}-12v=-62$$

Iddividi ż-żewġ naħat b'5.

$$\frac{5v^{2}-12v}{5}=-\frac{62}{5}$$

Meta tiddividi b'5 titneħħa l-multiplikazzjoni b'5.

$$v^{2}-\frac{12}{5}v=-\frac{62}{5}$$

Iddividi -\frac{12}{5}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{6}{5}. Imbagħad żid il-kwadru ta' -\frac{6}{5} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$v^{2}-\frac{12}{5}v+\left(-\frac{6}{5}\right)^{2}=-\frac{62}{5}+\left(-\frac{6}{5}\right)^{2}$$

Ikkwadra -\frac{6}{5} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{62}{5}+\frac{36}{25}$$

Żid -\frac{62}{5} ma' \frac{36}{25} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{274}{25}$$

Fattur v^{2}-\frac{12}{5}v+\frac{36}{25}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(v-\frac{6}{5}\right)^{2}=-\frac{274}{25}$$

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

$$\sqrt{\left(v-\frac{6}{5}\right)^{2}}=\sqrt{-\frac{274}{25}}$$

Issimplifika.

$$v-\frac{6}{5}=\frac{\sqrt{274}i}{5} v-\frac{6}{5}=-\frac{\sqrt{274}i}{5}$$

Żid \frac{6}{5} maż-żewġ naħat tal-ekwazzjoni.

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$