Réitigh (6v-9)(2v+1)=7v^2-38-33

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

Réitigh do v.

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

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

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Úsáid an t-airí dáileach chun 6v-9 a mhéadú faoi 2v+1 agus chun téarmaí comhchosúla a chumasc.

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

Dealaigh 33 ó -38 chun -71 a fháil.

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

Bain 7v^{2} ón dá thaobh.

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

Comhcheangail 12v^{2} agus -7v^{2} chun 5v^{2} a fháil.

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

Cuir 71 leis an dá thaobh.

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

Suimigh -9 agus 71 chun 62 a fháil.

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

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 5 in ionad a, -12 in ionad b, agus 62 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Cearnóg -12.

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

Méadaigh -4 faoi 5.

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

Méadaigh -20 faoi 62.

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

Suimigh 144 le -1240?

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

Tóg fréamh chearnach -1096.

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

Tá 12 urchomhairleach le -12.

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

Méadaigh 2 faoi 5.

$$v=\frac{12±2\sqrt{274}i}{10}$$

Réitigh an chothromóid v=\frac{12±2\sqrt{274}i}{10} nuair is ionann ± agus plus. Suimigh 12 le 2i\sqrt{274}?

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

Roinn 12+2i\sqrt{274} faoi 10.

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

Réitigh an chothromóid v=\frac{12±2\sqrt{274}i}{10} nuair is ionann ± agus míneas. Dealaigh 2i\sqrt{274} ó 12.

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

Roinn 12-2i\sqrt{274} faoi 10.

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

Tá an chothromóid réitithe anois.

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

Céimeanna chun an Chearnóg a Chomhlánú

Úsáid an t-airí dáileach chun 6v-9 a mhéadú faoi 2v+1 agus chun téarmaí comhchosúla a chumasc.

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

Dealaigh 33 ó -38 chun -71 a fháil.

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

Bain 7v^{2} ón dá thaobh.

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

Comhcheangail 12v^{2} agus -7v^{2} chun 5v^{2} a fháil.

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

Cuir 9 leis an dá thaobh.

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

Suimigh -71 agus 9 chun -62 a fháil.

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

Roinn an dá thaobh faoi 5.

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

Má roinntear é faoi 5 cuirtear an iolrúchán faoi 5 ar ceal.

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

Roinn -\frac{12}{5}, comhéifeacht an téarma x, faoi 2 chun -\frac{6}{5} a fháil. Ansin suimigh uimhir chearnach -\frac{6}{5} leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

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

Cearnaigh -\frac{6}{5} trí uimhreoir agus ainmneoir an chodáin a chearnú.

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

Suimigh -\frac{62}{5} le \frac{36}{25} trí chomhainmneoir a fháil agus na huimhreoirí a shuimiú. Laghdaigh an codán ansin go dtí na téarmaí is ísle más féidir.

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

Fachtóirigh v^{2}-\frac{12}{5}v+\frac{36}{25}. Go ginearálta, nuair x^{2}+bx+c cearnóg fhoirfe é, is féidir é a fhachtóiriú i gcónaí mar \left(x+\frac{b}{2}\right)^{2}.

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

Tóg fréamh chearnach an dá thaobh den chothromóid.

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

Simpligh.

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

Cuir \frac{6}{5} leis an dá thaobh den chothromóid.

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