Whakaoti i te -10x^2-x+8x-7+15x^2-9

$$- 10 x ^ { 2 } - x + 8 x - 7 + 15 x ^ { 2 } - 9$$

Aromātai

$$5x^{2}+7x-16$$

Ngā Upane Otinga

Pahekotia te -x me 8x, ka 7x.

$$-10x^{2}+7x-7+15x^{2}-9$$

Pahekotia te -10x^{2} me 15x^{2}, ka 5x^{2}.

$$5x^{2}+7x-7-9$$

Tangohia te 9 i te -7, ka -16.

$$5x^{2}+7x-16$$

Tauwehe

$$5\left(x-\frac{-3\sqrt{41}-7}{10}\right)\left(x-\frac{3\sqrt{41}-7}{10}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -x me 8x, ka 7x.

$$factor(-10x^{2}+7x-7+15x^{2}-9)$$

Pahekotia te -10x^{2} me 15x^{2}, ka 5x^{2}.

$$factor(5x^{2}+7x-7-9)$$

Tangohia te 9 i te -7, ka -16.

$$factor(5x^{2}+7x-16)$$

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.

$$5x^{2}+7x-16=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4\times 5\left(-16\right)}}{2\times 5}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 5\left(-16\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-7±\sqrt{49-20\left(-16\right)}}{2\times 5}$$

Whakareatia -20 ki te -16.

$$x=\frac{-7±\sqrt{49+320}}{2\times 5}$$

Tāpiri 49 ki te 320.

$$x=\frac{-7±\sqrt{369}}{2\times 5}$$

Tuhia te pūtakerua o te 369.

$$x=\frac{-7±3\sqrt{41}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-7±3\sqrt{41}}{10}$$

Nā, me whakaoti te whārite x=\frac{-7±3\sqrt{41}}{10} ina he tāpiri te ±. Tāpiri -7 ki te 3\sqrt{41}.

$$x=\frac{3\sqrt{41}-7}{10}$$

Nā, me whakaoti te whārite x=\frac{-7±3\sqrt{41}}{10} ina he tango te ±. Tango 3\sqrt{41} mai i -7.

$$x=\frac{-3\sqrt{41}-7}{10}$$

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+3\sqrt{41}}{10} mō te x_{1} me te \frac{-7-3\sqrt{41}}{10} mō te x_{2}.

$$5x^{2}+7x-16=5\left(x-\frac{3\sqrt{41}-7}{10}\right)\left(x-\frac{-3\sqrt{41}-7}{10}\right)$$