Whakaoti i te x^2+3x-4x^2-5x+6x^2-2x-3

$$x ^ { 2 } + 3 x - 4 x ^ { 2 } - 5 x + 6 x ^ { 2 } - 2 x - 3$$

Aromātai

$$3x^{2}-4x-3$$

Ngā Upane Otinga

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

$$-3x^{2}+3x-5x+6x^{2}-2x-3$$

Pahekotia te 3x me -5x, ka -2x.

$$-3x^{2}-2x+6x^{2}-2x-3$$

Pahekotia te -3x^{2} me 6x^{2}, ka 3x^{2}.

$$3x^{2}-2x-2x-3$$

Pahekotia te -2x me -2x, ka -4x.

$$3x^{2}-4x-3$$

Tauwehe

$$3\left(x-\frac{2-\sqrt{13}}{3}\right)\left(x-\frac{\sqrt{13}+2}{3}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$factor(-3x^{2}+3x-5x+6x^{2}-2x-3)$$

Pahekotia te 3x me -5x, ka -2x.

$$factor(-3x^{2}-2x+6x^{2}-2x-3)$$

Pahekotia te -3x^{2} me 6x^{2}, ka 3x^{2}.

$$factor(3x^{2}-2x-2x-3)$$

Pahekotia te -2x me -2x, ka -4x.

$$factor(3x^{2}-4x-3)$$

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.

$$3x^{2}-4x-3=0$$

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.

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

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 3\left(-3\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-4\right)±\sqrt{16-12\left(-3\right)}}{2\times 3}$$

Whakareatia -12 ki te -3.

$$x=\frac{-\left(-4\right)±\sqrt{16+36}}{2\times 3}$$

Tāpiri 16 ki te 36.

$$x=\frac{-\left(-4\right)±\sqrt{52}}{2\times 3}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-\left(-4\right)±2\sqrt{13}}{2\times 3}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2\sqrt{13}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{4±2\sqrt{13}}{6}$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{13}}{6} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}+4}{6}$$

Whakawehe 4+2\sqrt{13} ki te 6.

$$x=\frac{\sqrt{13}+2}{3}$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{13}}{6} ina he tango te ±. Tango 2\sqrt{13} mai i 4.

$$x=\frac{4-2\sqrt{13}}{6}$$

Whakawehe 4-2\sqrt{13} ki te 6.

$$x=\frac{2-\sqrt{13}}{3}$$

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{2+\sqrt{13}}{3} mō te x_{1} me te \frac{2-\sqrt{13}}{3} mō te x_{2}.

$$3x^{2}-4x-3=3\left(x-\frac{\sqrt{13}+2}{3}\right)\left(x-\frac{2-\sqrt{13}}{3}\right)$$