Whakaoti i te 9x^2+48x-64

$$9 { x }^{ 2 } +48x-64$$

Tauwehe

$$9\left(x-\frac{-8\sqrt{2}-8}{3}\right)\left(x-\frac{8\sqrt{2}-8}{3}\right)$$

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.

$$9x^{2}+48x-64=0$$

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.

$$x=\frac{-48±\sqrt{48^{2}-4\times 9\left(-64\right)}}{2\times 9}$$

Pūrua 48.

$$x=\frac{-48±\sqrt{2304-4\times 9\left(-64\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-48±\sqrt{2304-36\left(-64\right)}}{2\times 9}$$

Whakareatia -36 ki te -64.

$$x=\frac{-48±\sqrt{2304+2304}}{2\times 9}$$

Tāpiri 2304 ki te 2304.

$$x=\frac{-48±\sqrt{4608}}{2\times 9}$$

Tuhia te pūtakerua o te 4608.

$$x=\frac{-48±48\sqrt{2}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-48±48\sqrt{2}}{18}$$

Nā, me whakaoti te whārite x=\frac{-48±48\sqrt{2}}{18} ina he tāpiri te ±. Tāpiri -48 ki te 48\sqrt{2}.

$$x=\frac{48\sqrt{2}-48}{18}$$

Whakawehe -48+48\sqrt{2} ki te 18.

$$x=\frac{8\sqrt{2}-8}{3}$$

Nā, me whakaoti te whārite x=\frac{-48±48\sqrt{2}}{18} ina he tango te ±. Tango 48\sqrt{2} mai i -48.

$$x=\frac{-48\sqrt{2}-48}{18}$$

Whakawehe -48-48\sqrt{2} ki te 18.

$$x=\frac{-8\sqrt{2}-8}{3}$$

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{-8+8\sqrt{2}}{3} mō te x_{1} me te \frac{-8-8\sqrt{2}}{3} mō te x_{2}.

$$9x^{2}+48x-64=9\left(x-\frac{8\sqrt{2}-8}{3}\right)\left(x-\frac{-8\sqrt{2}-8}{3}\right)$$

Aromātai

$$9x^{2}+48x-64$$