Whakaoti i te 9x^2+9x-72

$$9 x ^ { 2 } + 9 x - 72$$

Tauwehe

$$9\left(x-\frac{-\sqrt{33}-1}{2}\right)\left(x-\frac{\sqrt{33}-1}{2}\right)$$

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.

$$9x^{2}+9x-72=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}-4\times 9\left(-72\right)}}{2\times 9}$$

Pūrua 9.

$$x=\frac{-9±\sqrt{81-4\times 9\left(-72\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-9±\sqrt{81-36\left(-72\right)}}{2\times 9}$$

Whakareatia -36 ki te -72.

$$x=\frac{-9±\sqrt{81+2592}}{2\times 9}$$

Tāpiri 81 ki te 2592.

$$x=\frac{-9±\sqrt{2673}}{2\times 9}$$

Tuhia te pūtakerua o te 2673.

$$x=\frac{-9±9\sqrt{33}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-9±9\sqrt{33}}{18}$$

Nā, me whakaoti te whārite x=\frac{-9±9\sqrt{33}}{18} ina he tāpiri te ±. Tāpiri -9 ki te 9\sqrt{33}.

$$x=\frac{9\sqrt{33}-9}{18}$$

Whakawehe -9+9\sqrt{33} ki te 18.

$$x=\frac{\sqrt{33}-1}{2}$$

Nā, me whakaoti te whārite x=\frac{-9±9\sqrt{33}}{18} ina he tango te ±. Tango 9\sqrt{33} mai i -9.

$$x=\frac{-9\sqrt{33}-9}{18}$$

Whakawehe -9-9\sqrt{33} ki te 18.

$$x=\frac{-\sqrt{33}-1}{2}$$

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{-1+\sqrt{33}}{2} mō te x_{1} me te \frac{-1-\sqrt{33}}{2} mō te x_{2}.

$$9x^{2}+9x-72=9\left(x-\frac{\sqrt{33}-1}{2}\right)\left(x-\frac{-\sqrt{33}-1}{2}\right)$$

Aromātai

$$9\left(x^{2}+x-8\right)$$