Whakaoti i te -x^2+16x-51

$$- { x }^{ 2 } +16x-51$$

Tauwehe

$$-\left(x-\left(8-\sqrt{13}\right)\right)\left(x-\left(\sqrt{13}+8\right)\right)$$

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.

$$-x^{2}+16x-51=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-1\right)\left(-51\right)}}{2\left(-1\right)}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-1\right)\left(-51\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-16±\sqrt{256+4\left(-51\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -51.

$$x=\frac{-16±\sqrt{256-204}}{2\left(-1\right)}$$

Tāpiri 256 ki te -204.

$$x=\frac{-16±\sqrt{52}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-16±2\sqrt{13}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-16±2\sqrt{13}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{13}}{-2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}-16}{-2}$$

Whakawehe -16+2\sqrt{13} ki te -2.

$$x=8-\sqrt{13}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{13}}{-2} ina he tango te ±. Tango 2\sqrt{13} mai i -16.

$$x=\frac{-2\sqrt{13}-16}{-2}$$

Whakawehe -16-2\sqrt{13} ki te -2.

$$x=\sqrt{13}+8$$

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 8-\sqrt{13} mō te x_{1} me te 8+\sqrt{13} mō te x_{2}.

$$-x^{2}+16x-51=-\left(x-\left(8-\sqrt{13}\right)\right)\left(x-\left(\sqrt{13}+8\right)\right)$$

Aromātai

$$-x^{2}+16x-51$$