Whakaoti i te f(x)=-x^2-16x+25

$$f ( x ) = - x ^ { 2 } - 16 x + 25$$

Tauwehe

$$-\left(x-\left(-\sqrt{89}-8\right)\right)\left(x-\left(\sqrt{89}-8\right)\right)$$

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.

$$-x^{2}-16x+25=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-16\right)±\sqrt{256+4\times 25}}{2\left(-1\right)}$$

Whakareatia 4 ki te 25.

$$x=\frac{-\left(-16\right)±\sqrt{256+100}}{2\left(-1\right)}$$

Tāpiri 256 ki te 100.

$$x=\frac{-\left(-16\right)±\sqrt{356}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 356.

$$x=\frac{-\left(-16\right)±2\sqrt{89}}{2\left(-1\right)}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±2\sqrt{89}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{16±2\sqrt{89}}{-2}$$

Nā, me whakaoti te whārite x=\frac{16±2\sqrt{89}}{-2} ina he tāpiri te ±. Tāpiri 16 ki te 2\sqrt{89}.

$$x=\frac{2\sqrt{89}+16}{-2}$$

Whakawehe 16+2\sqrt{89} ki te -2.

$$x=-\left(\sqrt{89}+8\right)$$

Nā, me whakaoti te whārite x=\frac{16±2\sqrt{89}}{-2} ina he tango te ±. Tango 2\sqrt{89} mai i 16.

$$x=\frac{16-2\sqrt{89}}{-2}$$

Whakawehe 16-2\sqrt{89} ki te -2.

$$x=\sqrt{89}-8$$

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 -\left(8+\sqrt{89}\right) mō te x_{1} me te -8+\sqrt{89} mō te x_{2}.

$$-x^{2}-16x+25=-\left(x-\left(-\left(\sqrt{89}+8\right)\right)\right)\left(x-\left(\sqrt{89}-8\right)\right)$$

Aromātai

$$25-16x-x^{2}$$