Whakaoti i te x^2+3x-4x^2+7x+12

$$x ^ { 2 } + 3 x - 4 x ^ { 2 } + 7 x + 12$$

Aromātai

$$12+10x-3x^{2}$$

Ngā Upane Otinga

Pahekotia te x^{2} me -4x^{2}, ka -3x^{2}.

$$-3x^{2}+3x+7x+12$$

Pahekotia te 3x me 7x, ka 10x.

$$-3x^{2}+10x+12$$

Tauwehe

$$-3\left(x-\frac{5-\sqrt{61}}{3}\right)\left(x-\frac{\sqrt{61}+5}{3}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x^{2} me -4x^{2}, ka -3x^{2}.

$$factor(-3x^{2}+3x+7x+12)$$

Pahekotia te 3x me 7x, ka 10x.

$$factor(-3x^{2}+10x+12)$$

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.

$$-3x^{2}+10x+12=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\left(-3\right)\times 12}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-10±\sqrt{100+12\times 12}}{2\left(-3\right)}$$

Whakareatia 12 ki te 12.

$$x=\frac{-10±\sqrt{100+144}}{2\left(-3\right)}$$

Tāpiri 100 ki te 144.

$$x=\frac{-10±\sqrt{244}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 244.

$$x=\frac{-10±2\sqrt{61}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-10±2\sqrt{61}}{-6}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{61}}{-6} ina he tāpiri te ±. Tāpiri -10 ki te 2\sqrt{61}.

$$x=\frac{2\sqrt{61}-10}{-6}$$

Whakawehe -10+2\sqrt{61} ki te -6.

$$x=\frac{5-\sqrt{61}}{3}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{61}}{-6} ina he tango te ±. Tango 2\sqrt{61} mai i -10.

$$x=\frac{-2\sqrt{61}-10}{-6}$$

Whakawehe -10-2\sqrt{61} ki te -6.

$$x=\frac{\sqrt{61}+5}{3}$$

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{61}}{3} mō te x_{1} me te \frac{5+\sqrt{61}}{3} mō te x_{2}.

$$-3x^{2}+10x+12=-3\left(x-\frac{5-\sqrt{61}}{3}\right)\left(x-\frac{\sqrt{61}+5}{3}\right)$$