Réitigh -(h^2+6h+9)-12h-4=0

$$- ( h ^ { 2 } + 6 h + 9 ) - 12 h - 4 = 0$$

Réitigh do h.

$$h=2\sqrt{17}-9\approx -0.753788749$$

$$h=-2\sqrt{17}-9\approx -17.246211251$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Chun an mhalairt ar h^{2}+6h+9 a aimsiú, aimsigh an mhalairt ar gach téarma.

$$-h^{2}-6h-9-12h-4=0$$

Comhcheangail -6h agus -12h chun -18h a fháil.

$$-h^{2}-18h-9-4=0$$

Dealaigh 4 ó -9 chun -13 a fháil.

$$-h^{2}-18h-13=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir -1 in ionad a, -18 in ionad b, agus -13 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\left(-1\right)\left(-13\right)}}{2\left(-1\right)}$$

Cearnóg -18.

$$h=\frac{-\left(-18\right)±\sqrt{324-4\left(-1\right)\left(-13\right)}}{2\left(-1\right)}$$

Méadaigh -4 faoi -1.

$$h=\frac{-\left(-18\right)±\sqrt{324+4\left(-13\right)}}{2\left(-1\right)}$$

Méadaigh 4 faoi -13.

$$h=\frac{-\left(-18\right)±\sqrt{324-52}}{2\left(-1\right)}$$

Suimigh 324 le -52?

$$h=\frac{-\left(-18\right)±\sqrt{272}}{2\left(-1\right)}$$

Tóg fréamh chearnach 272.

$$h=\frac{-\left(-18\right)±4\sqrt{17}}{2\left(-1\right)}$$

Tá 18 urchomhairleach le -18.

$$h=\frac{18±4\sqrt{17}}{2\left(-1\right)}$$

Méadaigh 2 faoi -1.

$$h=\frac{18±4\sqrt{17}}{-2}$$

Réitigh an chothromóid h=\frac{18±4\sqrt{17}}{-2} nuair is ionann ± agus plus. Suimigh 18 le 4\sqrt{17}?

$$h=\frac{4\sqrt{17}+18}{-2}$$

Roinn 18+4\sqrt{17} faoi -2.

$$h=-2\sqrt{17}-9$$

Réitigh an chothromóid h=\frac{18±4\sqrt{17}}{-2} nuair is ionann ± agus míneas. Dealaigh 4\sqrt{17} ó 18.

$$h=\frac{18-4\sqrt{17}}{-2}$$

Roinn 18-4\sqrt{17} faoi -2.

$$h=2\sqrt{17}-9$$

Tá an chothromóid réitithe anois.

$$h=-2\sqrt{17}-9 h=2\sqrt{17}-9$$

Céimeanna chun an Chearnóg a Chomhlánú

Chun an mhalairt ar h^{2}+6h+9 a aimsiú, aimsigh an mhalairt ar gach téarma.

$$-h^{2}-6h-9-12h-4=0$$

Comhcheangail -6h agus -12h chun -18h a fháil.

$$-h^{2}-18h-9-4=0$$

Dealaigh 4 ó -9 chun -13 a fháil.

$$-h^{2}-18h-13=0$$

Cuir 13 leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

$$-h^{2}-18h=13$$

Roinn an dá thaobh faoi -1.

$$\frac{-h^{2}-18h}{-1}=\frac{13}{-1}$$

Má roinntear é faoi -1 cuirtear an iolrúchán faoi -1 ar ceal.

$$h^{2}+\left(-\frac{18}{-1}\right)h=\frac{13}{-1}$$

Roinn -18 faoi -1.

$$h^{2}+18h=\frac{13}{-1}$$

Roinn 13 faoi -1.

$$h^{2}+18h=-13$$

Roinn 18, comhéifeacht an téarma x, faoi 2 chun 9 a fháil. Ansin suimigh uimhir chearnach 9 leis an dá thaobh den chothromóid. Déanann an chéim seo slánchearnóg de thaobh clé na cothromóide.

$$h^{2}+18h+9^{2}=-13+9^{2}$$

Cearnóg 9.

$$h^{2}+18h+81=-13+81$$

Suimigh -13 le 81?

$$h^{2}+18h+81=68$$

Fachtóirigh h^{2}+18h+81. 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}.

$$\left(h+9\right)^{2}=68$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$\sqrt{\left(h+9\right)^{2}}=\sqrt{68}$$

Simpligh.

$$h+9=2\sqrt{17} h+9=-2\sqrt{17}$$

Bain 9 ón dá thaobh den chothromóid.

$$h=2\sqrt{17}-9 h=-2\sqrt{17}-9$$