Whakaoti i te (-10x^2+x)+(-2x^2+9x+7)

$$( - 10 x ^ { 2 } + x ) + ( - 2 x ^ { 2 } + 9 x + 7 )$$

Aromātai

$$7+10x-12x^{2}$$

Ngā Upane Otinga

Pahekotia te -10x^{2} me -2x^{2}, ka -12x^{2}.

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

Pahekotia te x me 9x, ka 10x.

$$-12x^{2}+10x+7$$

Tauwehe

$$-12\left(x-\frac{5-\sqrt{109}}{12}\right)\left(x-\frac{\sqrt{109}+5}{12}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -10x^{2} me -2x^{2}, ka -12x^{2}.

$$factor(-12x^{2}+x+9x+7)$$

Pahekotia te x me 9x, ka 10x.

$$factor(-12x^{2}+10x+7)$$

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.

$$-12x^{2}+10x+7=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-12\right)\times 7}}{2\left(-12\right)}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\left(-12\right)\times 7}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{-10±\sqrt{100+48\times 7}}{2\left(-12\right)}$$

Whakareatia 48 ki te 7.

$$x=\frac{-10±\sqrt{100+336}}{2\left(-12\right)}$$

Tāpiri 100 ki te 336.

$$x=\frac{-10±\sqrt{436}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 436.

$$x=\frac{-10±2\sqrt{109}}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{-10±2\sqrt{109}}{-24}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{109}}{-24} ina he tāpiri te ±. Tāpiri -10 ki te 2\sqrt{109}.

$$x=\frac{2\sqrt{109}-10}{-24}$$

Whakawehe -10+2\sqrt{109} ki te -24.

$$x=\frac{5-\sqrt{109}}{12}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{109}}{-24} ina he tango te ±. Tango 2\sqrt{109} mai i -10.

$$x=\frac{-2\sqrt{109}-10}{-24}$$

Whakawehe -10-2\sqrt{109} ki te -24.

$$x=\frac{\sqrt{109}+5}{12}$$

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{5-\sqrt{109}}{12} mō te x_{1} me te \frac{5+\sqrt{109}}{12} mō te x_{2}.

$$-12x^{2}+10x+7=-12\left(x-\frac{5-\sqrt{109}}{12}\right)\left(x-\frac{\sqrt{109}+5}{12}\right)$$