Whakaoti i te 9x^2+16x-9

$$9 x ^ { 2 } + 16 x - 9$$

Tauwehe

$$9\left(x-\frac{-\sqrt{145}-8}{9}\right)\left(x-\frac{\sqrt{145}-8}{9}\right)$$

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.

$$9x^{2}+16x-9=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\times 9\left(-9\right)}}{2\times 9}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\times 9\left(-9\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-16±\sqrt{256-36\left(-9\right)}}{2\times 9}$$

Whakareatia -36 ki te -9.

$$x=\frac{-16±\sqrt{256+324}}{2\times 9}$$

Tāpiri 256 ki te 324.

$$x=\frac{-16±\sqrt{580}}{2\times 9}$$

Tuhia te pūtakerua o te 580.

$$x=\frac{-16±2\sqrt{145}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-16±2\sqrt{145}}{18}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{145}}{18} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{145}.

$$x=\frac{2\sqrt{145}-16}{18}$$

Whakawehe -16+2\sqrt{145} ki te 18.

$$x=\frac{\sqrt{145}-8}{9}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{145}}{18} ina he tango te ±. Tango 2\sqrt{145} mai i -16.

$$x=\frac{-2\sqrt{145}-16}{18}$$

Whakawehe -16-2\sqrt{145} ki te 18.

$$x=\frac{-\sqrt{145}-8}{9}$$

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+\sqrt{145}}{9} mō te x_{1} me te \frac{-8-\sqrt{145}}{9} mō te x_{2}.

$$9x^{2}+16x-9=9\left(x-\frac{\sqrt{145}-8}{9}\right)\left(x-\frac{-\sqrt{145}-8}{9}\right)$$

Aromātai

$$9x^{2}+16x-9$$