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

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

Tauwehe

$$\left(x-\left(-\sqrt{73}-8\right)\right)\left(x-\left(\sqrt{73}-8\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 25 i te 16, ka -9.

$$factor(x^{2}+16x-9)$$

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.

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

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.

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

Pūrua 16.

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

Whakareatia -4 ki te -9.

$$x=\frac{-16±\sqrt{256+36}}{2}$$

Tāpiri 256 ki te 36.

$$x=\frac{-16±\sqrt{292}}{2}$$

Tuhia te pūtakerua o te 292.

$$x=\frac{-16±2\sqrt{73}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{73}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{73}.

$$x=\frac{2\sqrt{73}-16}{2}$$

Whakawehe -16+2\sqrt{73} ki te 2.

$$x=\sqrt{73}-8$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{73}}{2} ina he tango te ±. Tango 2\sqrt{73} mai i -16.

$$x=\frac{-2\sqrt{73}-16}{2}$$

Whakawehe -16-2\sqrt{73} ki te 2.

$$x=-\sqrt{73}-8$$

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{73} mō te x_{1} me te -8-\sqrt{73} mō te x_{2}.

$$x^{2}+16x-9=\left(x-\left(\sqrt{73}-8\right)\right)\left(x-\left(-\sqrt{73}-8\right)\right)$$

Aromātai

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

Ngā Upane Otinga

Tangohia te 25 i te 16, ka -9.

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