Whakaoti i te -10-8x-x^2

$$- 10 - 8 x - x ^ { 2 }$$

Tauwehe

$$-\left(x-\left(-\sqrt{6}-4\right)\right)\left(x-\left(\sqrt{6}-4\right)\right)$$

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.

$$-x^{2}-8x-10=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -10.

$$x=\frac{-\left(-8\right)±\sqrt{64-40}}{2\left(-1\right)}$$

Tāpiri 64 ki te -40.

$$x=\frac{-\left(-8\right)±\sqrt{24}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-\left(-8\right)±2\sqrt{6}}{2\left(-1\right)}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±2\sqrt{6}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{8±2\sqrt{6}}{-2}$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{6}}{-2} ina he tāpiri te ±. Tāpiri 8 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}+8}{-2}$$

Whakawehe 8+2\sqrt{6} ki te -2.

$$x=-\left(\sqrt{6}+4\right)$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{6}}{-2} ina he tango te ±. Tango 2\sqrt{6} mai i 8.

$$x=\frac{8-2\sqrt{6}}{-2}$$

Whakawehe 8-2\sqrt{6} ki te -2.

$$x=\sqrt{6}-4$$

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(4+\sqrt{6}\right) mō te x_{1} me te -4+\sqrt{6} mō te x_{2}.

$$-x^{2}-8x-10=-\left(x-\left(-\left(\sqrt{6}+4\right)\right)\right)\left(x-\left(\sqrt{6}-4\right)\right)$$

Aromātai

$$-x^{2}-8x-10$$