Whakaoti i te -9x^2+6+11x^2-13-7x

$$- 9 x ^ { 2 } + 6 + 11 x ^ { 2 } - 13 - 7 x$$

Aromātai

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

Ngā Upane Otinga

Pahekotia te -9x^{2} me 11x^{2}, ka 2x^{2}.

$$2x^{2}+6-13-7x$$

Tangohia te 13 i te 6, ka -7.

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

Tauwehe

$$2\left(x-\frac{7-\sqrt{105}}{4}\right)\left(x-\frac{\sqrt{105}+7}{4}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -9x^{2} me 11x^{2}, ka 2x^{2}.

$$factor(2x^{2}+6-13-7x)$$

Tangohia te 13 i te 6, ka -7.

$$factor(2x^{2}-7-7x)$$

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.

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

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.

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

Pūrua -7.

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

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-7\right)±\sqrt{49-8\left(-7\right)}}{2\times 2}$$

Whakareatia -8 ki te -7.

$$x=\frac{-\left(-7\right)±\sqrt{49+56}}{2\times 2}$$

Tāpiri 49 ki te 56.

$$x=\frac{-\left(-7\right)±\sqrt{105}}{2\times 2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±\sqrt{105}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{7±\sqrt{105}}{4}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{105}}{4} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{105}.

$$x=\frac{\sqrt{105}+7}{4}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{105}}{4} ina he tango te ±. Tango \sqrt{105} mai i 7.

$$x=\frac{7-\sqrt{105}}{4}$$

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 \frac{7+\sqrt{105}}{4} mō te x_{1} me te \frac{7-\sqrt{105}}{4} mō te x_{2}.

$$2x^{2}-7x-7=2\left(x-\frac{\sqrt{105}+7}{4}\right)\left(x-\frac{7-\sqrt{105}}{4}\right)$$