Whakaoti i te 33x^2+74x+7-39x^2-88x+80

$$33 x ^ { 2 } + 74 x + 7 - 39 x ^ { 2 } - 88 x + 80$$

Aromātai

$$87-14x-6x^{2}$$

Ngā Upane Otinga

Pahekotia te 33x^{2} me -39x^{2}, ka -6x^{2}.

$$-6x^{2}+74x+7-88x+80$$

Pahekotia te 74x me -88x, ka -14x.

$$-6x^{2}-14x+7+80$$

Tāpirihia te 7 ki te 80, ka 87.

$$-6x^{2}-14x+87$$

Tauwehe

$$-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 33x^{2} me -39x^{2}, ka -6x^{2}.

$$factor(-6x^{2}+74x+7-88x+80)$$

Pahekotia te 74x me -88x, ka -14x.

$$factor(-6x^{2}-14x+7+80)$$

Tāpirihia te 7 ki te 80, ka 87.

$$factor(-6x^{2}-14x+87)$$

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.

$$-6x^{2}-14x+87=0$$

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.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\left(-6\right)\times 87}}{2\left(-6\right)}$$

Pūrua -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\left(-6\right)\times 87}}{2\left(-6\right)}$$

Whakareatia -4 ki te -6.

$$x=\frac{-\left(-14\right)±\sqrt{196+24\times 87}}{2\left(-6\right)}$$

Whakareatia 24 ki te 87.

$$x=\frac{-\left(-14\right)±\sqrt{196+2088}}{2\left(-6\right)}$$

Tāpiri 196 ki te 2088.

$$x=\frac{-\left(-14\right)±\sqrt{2284}}{2\left(-6\right)}$$

Tuhia te pūtakerua o te 2284.

$$x=\frac{-\left(-14\right)±2\sqrt{571}}{2\left(-6\right)}$$

Ko te tauaro o -14 ko 14.

$$x=\frac{14±2\sqrt{571}}{2\left(-6\right)}$$

Whakareatia 2 ki te -6.

$$x=\frac{14±2\sqrt{571}}{-12}$$

Nā, me whakaoti te whārite x=\frac{14±2\sqrt{571}}{-12} ina he tāpiri te ±. Tāpiri 14 ki te 2\sqrt{571}.

$$x=\frac{2\sqrt{571}+14}{-12}$$

Whakawehe 14+2\sqrt{571} ki te -12.

$$x=\frac{-\sqrt{571}-7}{6}$$

Nā, me whakaoti te whārite x=\frac{14±2\sqrt{571}}{-12} ina he tango te ±. Tango 2\sqrt{571} mai i 14.

$$x=\frac{14-2\sqrt{571}}{-12}$$

Whakawehe 14-2\sqrt{571} ki te -12.

$$x=\frac{\sqrt{571}-7}{6}$$

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{571}}{6} mō te x_{1} me te \frac{-7+\sqrt{571}}{6} mō te x_{2}.

$$-6x^{2}-14x+87=-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)$$