Whakaoti i te 3x^2+8x-14

$$3 { x }^{ 2 } +8x-14$$

Tauwehe

$$3\left(x-\frac{-\sqrt{58}-4}{3}\right)\left(x-\frac{\sqrt{58}-4}{3}\right)$$

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.

$$3x^{2}+8x-14=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 3\left(-14\right)}}{2\times 3}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 3\left(-14\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-8±\sqrt{64-12\left(-14\right)}}{2\times 3}$$

Whakareatia -12 ki te -14.

$$x=\frac{-8±\sqrt{64+168}}{2\times 3}$$

Tāpiri 64 ki te 168.

$$x=\frac{-8±\sqrt{232}}{2\times 3}$$

Tuhia te pūtakerua o te 232.

$$x=\frac{-8±2\sqrt{58}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-8±2\sqrt{58}}{6}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{58}}{6} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{58}.

$$x=\frac{2\sqrt{58}-8}{6}$$

Whakawehe -8+2\sqrt{58} ki te 6.

$$x=\frac{\sqrt{58}-4}{3}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{58}}{6} ina he tango te ±. Tango 2\sqrt{58} mai i -8.

$$x=\frac{-2\sqrt{58}-8}{6}$$

Whakawehe -8-2\sqrt{58} ki te 6.

$$x=\frac{-\sqrt{58}-4}{3}$$

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{-4+\sqrt{58}}{3} mō te x_{1} me te \frac{-4-\sqrt{58}}{3} mō te x_{2}.

$$3x^{2}+8x-14=3\left(x-\frac{\sqrt{58}-4}{3}\right)\left(x-\frac{-\sqrt{58}-4}{3}\right)$$

Aromātai

$$3x^{2}+8x-14$$