Réitigh 18=-1/5x^2+12x+32

$$18 = - \frac { 1 } { 5 } x ^ { 2 } + 12 x + 32$$

Réitigh do x.

$$x=\sqrt{970}+30\approx 61.144823005$$

$$x=30-\sqrt{970}\approx -1.144823005$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$-\frac{1}{5}x^{2}+12x+32=18$$

Bain 18 ón dá thaobh.

$$-\frac{1}{5}x^{2}+12x+32-18=0$$

Dealaigh 18 ó 32 chun 14 a fháil.

$$-\frac{1}{5}x^{2}+12x+14=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -\frac{1}{5} in ionad a, 12 in ionad b, agus 14 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

Cearnóg 12.

$$x=\frac{-12±\sqrt{144-4\left(-\frac{1}{5}\right)\times 14}}{2\left(-\frac{1}{5}\right)}$$

Méadaigh -4 faoi -\frac{1}{5}.

$$x=\frac{-12±\sqrt{144+\frac{4}{5}\times 14}}{2\left(-\frac{1}{5}\right)}$$

Méadaigh \frac{4}{5} faoi 14.

$$x=\frac{-12±\sqrt{144+\frac{56}{5}}}{2\left(-\frac{1}{5}\right)}$$

Suimigh 144 le \frac{56}{5}?

$$x=\frac{-12±\sqrt{\frac{776}{5}}}{2\left(-\frac{1}{5}\right)}$$

Tóg fréamh chearnach \frac{776}{5}.

$$x=\frac{-12±\frac{2\sqrt{970}}{5}}{2\left(-\frac{1}{5}\right)}$$

Méadaigh 2 faoi -\frac{1}{5}.

$$x=\frac{-12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}}$$

Réitigh an chothromóid x=\frac{-12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} nuair is ionann ± agus plus. Suimigh -12 le \frac{2\sqrt{970}}{5}?

$$x=\frac{\frac{2\sqrt{970}}{5}-12}{-\frac{2}{5}}$$

Roinn -12+\frac{2\sqrt{970}}{5} faoi -\frac{2}{5} trí -12+\frac{2\sqrt{970}}{5} a mhéadú faoi dheilín -\frac{2}{5}.

$$x=30-\sqrt{970}$$

Réitigh an chothromóid x=\frac{-12±\frac{2\sqrt{970}}{5}}{-\frac{2}{5}} nuair is ionann ± agus míneas. Dealaigh \frac{2\sqrt{970}}{5} ó -12.

$$x=\frac{-\frac{2\sqrt{970}}{5}-12}{-\frac{2}{5}}$$

Roinn -12-\frac{2\sqrt{970}}{5} faoi -\frac{2}{5} trí -12-\frac{2\sqrt{970}}{5} a mhéadú faoi dheilín -\frac{2}{5}.

$$x=\sqrt{970}+30$$

Tá an chothromóid réitithe anois.

$$x=30-\sqrt{970} x=\sqrt{970}+30$$

Céimeanna chun an Chearnóg a Chomhlánú

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$-\frac{1}{5}x^{2}+12x+32=18$$

Bain 32 ón dá thaobh.

$$-\frac{1}{5}x^{2}+12x=18-32$$

Dealaigh 32 ó 18 chun -14 a fháil.

$$-\frac{1}{5}x^{2}+12x=-14$$

Iolraigh an dá thaobh faoi -5.

$$\frac{-\frac{1}{5}x^{2}+12x}{-\frac{1}{5}}=-\frac{14}{-\frac{1}{5}}$$

Má roinntear é faoi -\frac{1}{5} cuirtear an iolrúchán faoi -\frac{1}{5} ar ceal.

$$x^{2}+\frac{12}{-\frac{1}{5}}x=-\frac{14}{-\frac{1}{5}}$$

Roinn 12 faoi -\frac{1}{5} trí 12 a mhéadú faoi dheilín -\frac{1}{5}.

$$x^{2}-60x=-\frac{14}{-\frac{1}{5}}$$

Roinn -14 faoi -\frac{1}{5} trí -14 a mhéadú faoi dheilín -\frac{1}{5}.

$$x^{2}-60x=70$$

Roinn -60, comhéifeacht an téarma x, faoi 2 chun -30 a fháil. Ansin suimigh uimhir chearnach -30 leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$x^{2}-60x+\left(-30\right)^{2}=70+\left(-30\right)^{2}$$

Cearnóg -30.

$$x^{2}-60x+900=70+900$$

Suimigh 70 le 900?

$$x^{2}-60x+900=970$$

Fachtóirigh x^{2}-60x+900. 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}.

$$\left(x-30\right)^{2}=970$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{970}$$

Simpligh.

$$x-30=\sqrt{970} x-30=-\sqrt{970}$$

Cuir 30 leis an dá thaobh den chothromóid.

$$x=\sqrt{970}+30 x=30-\sqrt{970}$$