Whakaoti i te 8x^2+3-4x-5x^2-9x

$$8 { x }^{ 2 } +3-4x-5 { x }^{ 2 } -9x$$

Aromātai

$$3x^{2}-13x+3$$

Ngā Upane Otinga

Pahekotia te 8x^{2} me -5x^{2}, ka 3x^{2}.

$$3x^{2}+3-4x-9x$$

Pahekotia te -4x me -9x, ka -13x.

$$3x^{2}+3-13x$$

Tauwehe

$$3\left(x-\frac{13-\sqrt{133}}{6}\right)\left(x-\frac{\sqrt{133}+13}{6}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 8x^{2} me -5x^{2}, ka 3x^{2}.

$$factor(3x^{2}+3-4x-9x)$$

Pahekotia te -4x me -9x, ka -13x.

$$factor(3x^{2}+3-13x)$$

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.

$$3x^{2}-13x+3=0$$

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.

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

Pūrua -13.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 3\times 3}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-13\right)±\sqrt{169-12\times 3}}{2\times 3}$$

Whakareatia -12 ki te 3.

$$x=\frac{-\left(-13\right)±\sqrt{169-36}}{2\times 3}$$

Tāpiri 169 ki te -36.

$$x=\frac{-\left(-13\right)±\sqrt{133}}{2\times 3}$$

Ko te tauaro o -13 ko 13.

$$x=\frac{13±\sqrt{133}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{13±\sqrt{133}}{6}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{133}}{6} ina he tāpiri te ±. Tāpiri 13 ki te \sqrt{133}.

$$x=\frac{\sqrt{133}+13}{6}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{133}}{6} ina he tango te ±. Tango \sqrt{133} mai i 13.

$$x=\frac{13-\sqrt{133}}{6}$$

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{13+\sqrt{133}}{6} mō te x_{1} me te \frac{13-\sqrt{133}}{6} mō te x_{2}.

$$3x^{2}-13x+3=3\left(x-\frac{\sqrt{133}+13}{6}\right)\left(x-\frac{13-\sqrt{133}}{6}\right)$$