Whakaoti i te 9x^2+12x-2

$$9 { x }^{ 2 } +12x-2$$

Tauwehe

$$9\left(x-\frac{-\sqrt{6}-2}{3}\right)\left(x-\frac{\sqrt{6}-2}{3}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$9x^{2}+12x-2=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x=\frac{-12±\sqrt{12^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 9\left(-2\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-12±\sqrt{144-36\left(-2\right)}}{2\times 9}$$

Whakareatia -36 ki te -2.

$$x=\frac{-12±\sqrt{144+72}}{2\times 9}$$

Tāpiri 144 ki te 72.

$$x=\frac{-12±\sqrt{216}}{2\times 9}$$

Tuhia te pūtakerua o te 216.

$$x=\frac{-12±6\sqrt{6}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-12±6\sqrt{6}}{18}$$

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{6}}{18} ina he tāpiri te ±. Tāpiri -12 ki te 6\sqrt{6}.

$$x=\frac{6\sqrt{6}-12}{18}$$

Whakawehe -12+6\sqrt{6} ki te 18.

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

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{6}}{18} ina he tango te ±. Tango 6\sqrt{6} mai i -12.

$$x=\frac{-6\sqrt{6}-12}{18}$$

Whakawehe -12-6\sqrt{6} ki te 18.

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

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{-2+\sqrt{6}}{3} mō te x_{1} me te \frac{-2-\sqrt{6}}{3} mō te x_{2}.

$$9x^{2}+12x-2=9\left(x-\frac{\sqrt{6}-2}{3}\right)\left(x-\frac{-\sqrt{6}-2}{3}\right)$$

Aromātai

$$9x^{2}+12x-2$$