Whakaoti i te 18x^2+31x-40

$$18 x ^ { 2 } + 31 x - 40$$

Tauwehe

$$18\left(x-\frac{-\sqrt{3841}-31}{36}\right)\left(x-\frac{\sqrt{3841}-31}{36}\right)$$

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.

$$18x^{2}+31x-40=0$$

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.

$$x=\frac{-31±\sqrt{31^{2}-4\times 18\left(-40\right)}}{2\times 18}$$

Pūrua 31.

$$x=\frac{-31±\sqrt{961-4\times 18\left(-40\right)}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$x=\frac{-31±\sqrt{961-72\left(-40\right)}}{2\times 18}$$

Whakareatia -72 ki te -40.

$$x=\frac{-31±\sqrt{961+2880}}{2\times 18}$$

Tāpiri 961 ki te 2880.

$$x=\frac{-31±\sqrt{3841}}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{-31±\sqrt{3841}}{36}$$

Nā, me whakaoti te whārite x=\frac{-31±\sqrt{3841}}{36} ina he tāpiri te ±. Tāpiri -31 ki te \sqrt{3841}.

$$x=\frac{\sqrt{3841}-31}{36}$$

Nā, me whakaoti te whārite x=\frac{-31±\sqrt{3841}}{36} ina he tango te ±. Tango \sqrt{3841} mai i -31.

$$x=\frac{-\sqrt{3841}-31}{36}$$

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{-31+\sqrt{3841}}{36} mō te x_{1} me te \frac{-31-\sqrt{3841}}{36} mō te x_{2}.

$$18x^{2}+31x-40=18\left(x-\frac{\sqrt{3841}-31}{36}\right)\left(x-\frac{-\sqrt{3841}-31}{36}\right)$$

Aromātai

$$18x^{2}+31x-40$$