Whakaoti i te 2x^2-18x+20

$$2 x ^ { 2 } - 18 x + 20$$

Tauwehe

$$2\left(x-\frac{9-\sqrt{41}}{2}\right)\left(x-\frac{\sqrt{41}+9}{2}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$2x^{2}-18x+20=0$$

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.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 2\times 20}}{2\times 2}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 2\times 20}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-18\right)±\sqrt{324-8\times 20}}{2\times 2}$$

Whakareatia -8 ki te 20.

$$x=\frac{-\left(-18\right)±\sqrt{324-160}}{2\times 2}$$

Tāpiri 324 ki te -160.

$$x=\frac{-\left(-18\right)±\sqrt{164}}{2\times 2}$$

Tuhia te pūtakerua o te 164.

$$x=\frac{-\left(-18\right)±2\sqrt{41}}{2\times 2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±2\sqrt{41}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{18±2\sqrt{41}}{4}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{41}}{4} ina he tāpiri te ±. Tāpiri 18 ki te 2\sqrt{41}.

$$x=\frac{2\sqrt{41}+18}{4}$$

Whakawehe 18+2\sqrt{41} ki te 4.

$$x=\frac{\sqrt{41}+9}{2}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{41}}{4} ina he tango te ±. Tango 2\sqrt{41} mai i 18.

$$x=\frac{18-2\sqrt{41}}{4}$$

Whakawehe 18-2\sqrt{41} ki te 4.

$$x=\frac{9-\sqrt{41}}{2}$$

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{9+\sqrt{41}}{2} mō te x_{1} me te \frac{9-\sqrt{41}}{2} mō te x_{2}.

$$2x^{2}-18x+20=2\left(x-\frac{\sqrt{41}+9}{2}\right)\left(x-\frac{9-\sqrt{41}}{2}\right)$$

Aromātai

$$2\left(x^{2}-9x+10\right)$$