Whakaoti i te 2x^2-3x-5*2x+3

$$2 { x }^{ 2 } -3x-5 \times 2x+3$$

Aromātai

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

Ngā Upane Otinga

Whakareatia te 5 ki te 2, ka 10.

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

Pahekotia te -3x me -10x, ka -13x.

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

Tauwehe

$$2\left(x-\frac{13-\sqrt{145}}{4}\right)\left(x-\frac{\sqrt{145}+13}{4}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 5 ki te 2, ka 10.

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

Pahekotia te -3x me -10x, ka -13x.

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

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.

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

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.

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

Pūrua -13.

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

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-13\right)±\sqrt{169-8\times 3}}{2\times 2}$$

Whakareatia -8 ki te 3.

$$x=\frac{-\left(-13\right)±\sqrt{169-24}}{2\times 2}$$

Tāpiri 169 ki te -24.

$$x=\frac{-\left(-13\right)±\sqrt{145}}{2\times 2}$$

Ko te tauaro o -13 ko 13.

$$x=\frac{13±\sqrt{145}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{13±\sqrt{145}}{4}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{145}}{4} ina he tāpiri te ±. Tāpiri 13 ki te \sqrt{145}.

$$x=\frac{\sqrt{145}+13}{4}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{145}}{4} ina he tango te ±. Tango \sqrt{145} mai i 13.

$$x=\frac{13-\sqrt{145}}{4}$$

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{145}}{4} mō te x_{1} me te \frac{13-\sqrt{145}}{4} mō te x_{2}.

$$2x^{2}-13x+3=2\left(x-\frac{\sqrt{145}+13}{4}\right)\left(x-\frac{13-\sqrt{145}}{4}\right)$$