Whakaoti i te 18x^2+32x-16

$$18 { x }^{ 2 } +32x-16$$

Tauwehe

$$18\left(x-\frac{-2\sqrt{34}-8}{9}\right)\left(x-\frac{2\sqrt{34}-8}{9}\right)$$

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.

$$18x^{2}+32x-16=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4\times 18\left(-16\right)}}{2\times 18}$$

Pūrua 32.

$$x=\frac{-32±\sqrt{1024-4\times 18\left(-16\right)}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$x=\frac{-32±\sqrt{1024-72\left(-16\right)}}{2\times 18}$$

Whakareatia -72 ki te -16.

$$x=\frac{-32±\sqrt{1024+1152}}{2\times 18}$$

Tāpiri 1024 ki te 1152.

$$x=\frac{-32±\sqrt{2176}}{2\times 18}$$

Tuhia te pūtakerua o te 2176.

$$x=\frac{-32±8\sqrt{34}}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{-32±8\sqrt{34}}{36}$$

Nā, me whakaoti te whārite x=\frac{-32±8\sqrt{34}}{36} ina he tāpiri te ±. Tāpiri -32 ki te 8\sqrt{34}.

$$x=\frac{8\sqrt{34}-32}{36}$$

Whakawehe -32+8\sqrt{34} ki te 36.

$$x=\frac{2\sqrt{34}-8}{9}$$

Nā, me whakaoti te whārite x=\frac{-32±8\sqrt{34}}{36} ina he tango te ±. Tango 8\sqrt{34} mai i -32.

$$x=\frac{-8\sqrt{34}-32}{36}$$

Whakawehe -32-8\sqrt{34} ki te 36.

$$x=\frac{-2\sqrt{34}-8}{9}$$

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{-8+2\sqrt{34}}{9} mō te x_{1} me te \frac{-8-2\sqrt{34}}{9} mō te x_{2}.

$$18x^{2}+32x-16=18\left(x-\frac{2\sqrt{34}-8}{9}\right)\left(x-\frac{-2\sqrt{34}-8}{9}\right)$$

Aromātai

$$18x^{2}+32x-16$$