Réitigh 144y^2-5=30

$$144 y ^ { 2 } - 5 = 30$$

Réitigh do y.

$$y=\frac{\sqrt{35}}{12}\approx 0.493006649$$

$$y=-\frac{\sqrt{35}}{12}\approx -0.493006649$$

Céimeanna tríd an bhFréamh Chearnach a Fháil

Cuir 5 leis an dá thaobh.

$$144y^{2}=30+5$$

Suimigh 30 agus 5 chun 35 a fháil.

$$144y^{2}=35$$

Roinn an dá thaobh faoi 144.

$$y^{2}=\frac{35}{144}$$

Tóg fréamh chearnach an dá thaobh den chothromóid.

$$y=\frac{\sqrt{35}}{12} y=-\frac{\sqrt{35}}{12}$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Bain 30 ón dá thaobh.

$$144y^{2}-5-30=0$$

Dealaigh 30 ó -5 chun -35 a fháil.

$$144y^{2}-35=0$$

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 144 in ionad a, 0 in ionad b, agus -35 in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 144\left(-35\right)}}{2\times 144}$$

Cearnóg 0.

$$y=\frac{0±\sqrt{-4\times 144\left(-35\right)}}{2\times 144}$$

Méadaigh -4 faoi 144.

$$y=\frac{0±\sqrt{-576\left(-35\right)}}{2\times 144}$$

Méadaigh -576 faoi -35.

$$y=\frac{0±\sqrt{20160}}{2\times 144}$$

Tóg fréamh chearnach 20160.

$$y=\frac{0±24\sqrt{35}}{2\times 144}$$

Méadaigh 2 faoi 144.

$$y=\frac{0±24\sqrt{35}}{288}$$

Réitigh an chothromóid y=\frac{0±24\sqrt{35}}{288} nuair is ionann ± agus plus.

$$y=\frac{\sqrt{35}}{12}$$

Réitigh an chothromóid y=\frac{0±24\sqrt{35}}{288} nuair is ionann ± agus míneas.

$$y=-\frac{\sqrt{35}}{12}$$

Tá an chothromóid réitithe anois.

$$y=\frac{\sqrt{35}}{12} y=-\frac{\sqrt{35}}{12}$$