Réitigh 27x^2-9x-1

$$27 x ^ { 2 } - 9 x - 1$$

Fachtóirigh

$$27\left(x-\left(-\frac{\sqrt{21}}{18}+\frac{1}{6}\right)\right)\left(x-\left(\frac{\sqrt{21}}{18}+\frac{1}{6}\right)\right)$$

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.

$$27x^{2}-9x-1=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 27\left(-1\right)}}{2\times 27}$$

Cearnóg -9.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 27\left(-1\right)}}{2\times 27}$$

Méadaigh -4 faoi 27.

$$x=\frac{-\left(-9\right)±\sqrt{81-108\left(-1\right)}}{2\times 27}$$

Méadaigh -108 faoi -1.

$$x=\frac{-\left(-9\right)±\sqrt{81+108}}{2\times 27}$$

Suimigh 81 le 108?

$$x=\frac{-\left(-9\right)±\sqrt{189}}{2\times 27}$$

Tóg fréamh chearnach 189.

$$x=\frac{-\left(-9\right)±3\sqrt{21}}{2\times 27}$$

Tá 9 urchomhairleach le -9.

$$x=\frac{9±3\sqrt{21}}{2\times 27}$$

Méadaigh 2 faoi 27.

$$x=\frac{9±3\sqrt{21}}{54}$$

Réitigh an chothromóid x=\frac{9±3\sqrt{21}}{54} nuair is ionann ± agus plus. Suimigh 9 le 3\sqrt{21}?

$$x=\frac{3\sqrt{21}+9}{54}$$

Roinn 9+3\sqrt{21} faoi 54.

$$x=\frac{\sqrt{21}}{18}+\frac{1}{6}$$

Réitigh an chothromóid x=\frac{9±3\sqrt{21}}{54} nuair is ionann ± agus míneas. Dealaigh 3\sqrt{21} ó 9.

$$x=\frac{9-3\sqrt{21}}{54}$$

Roinn 9-3\sqrt{21} faoi 54.

$$x=-\frac{\sqrt{21}}{18}+\frac{1}{6}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir \frac{1}{6}+\frac{\sqrt{21}}{18} in ionad x_{1} agus \frac{1}{6}-\frac{\sqrt{21}}{18} in ionad x_{2}.

$$27x^{2}-9x-1=27\left(x-\left(\frac{\sqrt{21}}{18}+\frac{1}{6}\right)\right)\left(x-\left(-\frac{\sqrt{21}}{18}+\frac{1}{6}\right)\right)$$

Luacháil

$$27x^{2}-9x-1$$