Whakaoti i te -9x^2-12x-8x^2+7+15x

$$- 9 x ^ { 2 } - 12 x - 8 x ^ { 2 } + 7 + 15 x$$

Aromātai

$$7+3x-17x^{2}$$

Ngā Upane Otinga

Pahekotia te -9x^{2} me -8x^{2}, ka -17x^{2}.

$$-17x^{2}-12x+7+15x$$

Pahekotia te -12x me 15x, ka 3x.

$$-17x^{2}+3x+7$$

Tauwehe

$$-17\left(x-\frac{3-\sqrt{485}}{34}\right)\left(x-\frac{\sqrt{485}+3}{34}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -9x^{2} me -8x^{2}, ka -17x^{2}.

$$factor(-17x^{2}-12x+7+15x)$$

Pahekotia te -12x me 15x, ka 3x.

$$factor(-17x^{2}+3x+7)$$

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.

$$-17x^{2}+3x+7=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-17\right)\times 7}}{2\left(-17\right)}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-17\right)\times 7}}{2\left(-17\right)}$$

Whakareatia -4 ki te -17.

$$x=\frac{-3±\sqrt{9+68\times 7}}{2\left(-17\right)}$$

Whakareatia 68 ki te 7.

$$x=\frac{-3±\sqrt{9+476}}{2\left(-17\right)}$$

Tāpiri 9 ki te 476.

$$x=\frac{-3±\sqrt{485}}{2\left(-17\right)}$$

Whakareatia 2 ki te -17.

$$x=\frac{-3±\sqrt{485}}{-34}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{485}}{-34} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{485}.

$$x=\frac{\sqrt{485}-3}{-34}$$

Whakawehe -3+\sqrt{485} ki te -34.

$$x=\frac{3-\sqrt{485}}{34}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{485}}{-34} ina he tango te ±. Tango \sqrt{485} mai i -3.

$$x=\frac{-\sqrt{485}-3}{-34}$$

Whakawehe -3-\sqrt{485} ki te -34.

$$x=\frac{\sqrt{485}+3}{34}$$

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{3-\sqrt{485}}{34} mō te x_{1} me te \frac{3+\sqrt{485}}{34} mō te x_{2}.

$$-17x^{2}+3x+7=-17\left(x-\frac{3-\sqrt{485}}{34}\right)\left(x-\frac{\sqrt{485}+3}{34}\right)$$