Whakaoti i te -x^2-7x+5

$$- x ^ { 2 } - 7 x + 5$$

Tauwehe

$$-\left(x-\frac{-\sqrt{69}-7}{2}\right)\left(x-\frac{\sqrt{69}-7}{2}\right)$$

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.

$$-x^{2}-7x+5=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-7\right)±\sqrt{49+4\times 5}}{2\left(-1\right)}$$

Whakareatia 4 ki te 5.

$$x=\frac{-\left(-7\right)±\sqrt{49+20}}{2\left(-1\right)}$$

Tāpiri 49 ki te 20.

$$x=\frac{-\left(-7\right)±\sqrt{69}}{2\left(-1\right)}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±\sqrt{69}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{7±\sqrt{69}}{-2}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{69}}{-2} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{69}.

$$x=\frac{\sqrt{69}+7}{-2}$$

Whakawehe 7+\sqrt{69} ki te -2.

$$x=\frac{-\sqrt{69}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{69}}{-2} ina he tango te ±. Tango \sqrt{69} mai i 7.

$$x=\frac{7-\sqrt{69}}{-2}$$

Whakawehe 7-\sqrt{69} ki te -2.

$$x=\frac{\sqrt{69}-7}{2}$$

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{-7-\sqrt{69}}{2} mō te x_{1} me te \frac{-7+\sqrt{69}}{2} mō te x_{2}.

$$-x^{2}-7x+5=-\left(x-\frac{-\sqrt{69}-7}{2}\right)\left(x-\frac{\sqrt{69}-7}{2}\right)$$

Aromātai

$$5-7x-x^{2}$$