Whakaoti i te =-3x^2-8x-3

$$= - 3 x ^ { 2 } - 8 x - 3$$

Tauwehe

$$-3\left(x-\frac{-\sqrt{7}-4}{3}\right)\left(x-\frac{\sqrt{7}-4}{3}\right)$$

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.

$$-3x^{2}-8x-3=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-3\right)\left(-3\right)}}{2\left(-3\right)}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-3\right)\left(-3\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-\left(-8\right)±\sqrt{64+12\left(-3\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -3.

$$x=\frac{-\left(-8\right)±\sqrt{64-36}}{2\left(-3\right)}$$

Tāpiri 64 ki te -36.

$$x=\frac{-\left(-8\right)±\sqrt{28}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 28.

$$x=\frac{-\left(-8\right)±2\sqrt{7}}{2\left(-3\right)}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±2\sqrt{7}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{8±2\sqrt{7}}{-6}$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{7}}{-6} ina he tāpiri te ±. Tāpiri 8 ki te 2\sqrt{7}.

$$x=\frac{2\sqrt{7}+8}{-6}$$

Whakawehe 8+2\sqrt{7} ki te -6.

$$x=\frac{-\sqrt{7}-4}{3}$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{7}}{-6} ina he tango te ±. Tango 2\sqrt{7} mai i 8.

$$x=\frac{8-2\sqrt{7}}{-6}$$

Whakawehe 8-2\sqrt{7} ki te -6.

$$x=\frac{\sqrt{7}-4}{3}$$

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{-4-\sqrt{7}}{3} mō te x_{1} me te \frac{-4+\sqrt{7}}{3} mō te x_{2}.

$$-3x^{2}-8x-3=-3\left(x-\frac{-\sqrt{7}-4}{3}\right)\left(x-\frac{\sqrt{7}-4}{3}\right)$$

Aromātai

$$-3x^{2}-8x-3$$