Réitigh 18x^2+24x+7

$$18 x ^ { 2 } + 24 x + 7$$

Fachtóirigh

$$18\left(x-\left(-\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)\left(x-\left(\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)$$

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.

$$18x^{2}+24x+7=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}-4\times 18\times 7}}{2\times 18}$$

Cearnóg 24.

$$x=\frac{-24±\sqrt{576-4\times 18\times 7}}{2\times 18}$$

Méadaigh -4 faoi 18.

$$x=\frac{-24±\sqrt{576-72\times 7}}{2\times 18}$$

Méadaigh -72 faoi 7.

$$x=\frac{-24±\sqrt{576-504}}{2\times 18}$$

Suimigh 576 le -504?

$$x=\frac{-24±\sqrt{72}}{2\times 18}$$

Tóg fréamh chearnach 72.

$$x=\frac{-24±6\sqrt{2}}{2\times 18}$$

Méadaigh 2 faoi 18.

$$x=\frac{-24±6\sqrt{2}}{36}$$

Réitigh an chothromóid x=\frac{-24±6\sqrt{2}}{36} nuair is ionann ± agus plus. Suimigh -24 le 6\sqrt{2}?

$$x=\frac{6\sqrt{2}-24}{36}$$

Roinn -24+6\sqrt{2} faoi 36.

$$x=\frac{\sqrt{2}}{6}-\frac{2}{3}$$

Réitigh an chothromóid x=\frac{-24±6\sqrt{2}}{36} nuair is ionann ± agus míneas. Dealaigh 6\sqrt{2} ó -24.

$$x=\frac{-6\sqrt{2}-24}{36}$$

Roinn -24-6\sqrt{2} faoi 36.

$$x=-\frac{\sqrt{2}}{6}-\frac{2}{3}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir -\frac{2}{3}+\frac{\sqrt{2}}{6} in ionad x_{1} agus -\frac{2}{3}-\frac{\sqrt{2}}{6} in ionad x_{2}.

$$18x^{2}+24x+7=18\left(x-\left(\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)\left(x-\left(-\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)$$

Luacháil

$$18x^{2}+24x+7$$