Réitigh 65y^2-23y-10

$$65 y ^ { 2 } - 23 y - 10$$

Fachtóirigh

$$65\left(y-\frac{23-\sqrt{3129}}{130}\right)\left(y-\frac{\sqrt{3129}+23}{130}\right)$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Is féidir an trasfhoirmiú ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) a úsáid chun luach iltéarmach cearnach a fhachtóiriú, nuair is réitigh iad x_{1} agus x_{2} ar an gcothromóid chearnach ax^{2}+bx+c=0.

$$65y^{2}-23y-10=0$$

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

$$y=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\times 65\left(-10\right)}}{2\times 65}$$

Cearnóg -23.

$$y=\frac{-\left(-23\right)±\sqrt{529-4\times 65\left(-10\right)}}{2\times 65}$$

Méadaigh -4 faoi 65.

$$y=\frac{-\left(-23\right)±\sqrt{529-260\left(-10\right)}}{2\times 65}$$

Méadaigh -260 faoi -10.

$$y=\frac{-\left(-23\right)±\sqrt{529+2600}}{2\times 65}$$

Suimigh 529 le 2600?

$$y=\frac{-\left(-23\right)±\sqrt{3129}}{2\times 65}$$

Tá 23 urchomhairleach le -23.

$$y=\frac{23±\sqrt{3129}}{2\times 65}$$

Méadaigh 2 faoi 65.

$$y=\frac{23±\sqrt{3129}}{130}$$

Réitigh an chothromóid y=\frac{23±\sqrt{3129}}{130} nuair is ionann ± agus plus. Suimigh 23 le \sqrt{3129}?

$$y=\frac{\sqrt{3129}+23}{130}$$

Réitigh an chothromóid y=\frac{23±\sqrt{3129}}{130} nuair is ionann ± agus míneas. Dealaigh \sqrt{3129} ó 23.

$$y=\frac{23-\sqrt{3129}}{130}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir \frac{23+\sqrt{3129}}{130} in ionad x_{1} agus \frac{23-\sqrt{3129}}{130} in ionad x_{2}.

$$65y^{2}-23y-10=65\left(y-\frac{\sqrt{3129}+23}{130}\right)\left(y-\frac{23-\sqrt{3129}}{130}\right)$$

Luacháil

$$65y^{2}-23y-10$$