Whakaoti i te 4x^2+14x-12

$$4 x ^ { 2 } + 14 x - 12$$

Tauwehe

$$4\left(x-\frac{-\sqrt{97}-7}{4}\right)\left(x-\frac{\sqrt{97}-7}{4}\right)$$

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.

$$4x^{2}+14x-12=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 4\left(-12\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-14±\sqrt{196-16\left(-12\right)}}{2\times 4}$$

Whakareatia -16 ki te -12.

$$x=\frac{-14±\sqrt{196+192}}{2\times 4}$$

Tāpiri 196 ki te 192.

$$x=\frac{-14±\sqrt{388}}{2\times 4}$$

Tuhia te pūtakerua o te 388.

$$x=\frac{-14±2\sqrt{97}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-14±2\sqrt{97}}{8}$$

Nā, me whakaoti te whārite x=\frac{-14±2\sqrt{97}}{8} ina he tāpiri te ±. Tāpiri -14 ki te 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-14}{8}$$

Whakawehe -14+2\sqrt{97} ki te 8.

$$x=\frac{\sqrt{97}-7}{4}$$

Nā, me whakaoti te whārite x=\frac{-14±2\sqrt{97}}{8} ina he tango te ±. Tango 2\sqrt{97} mai i -14.

$$x=\frac{-2\sqrt{97}-14}{8}$$

Whakawehe -14-2\sqrt{97} ki te 8.

$$x=\frac{-\sqrt{97}-7}{4}$$

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{-7+\sqrt{97}}{4} mō te x_{1} me te \frac{-7-\sqrt{97}}{4} mō te x_{2}.

$$4x^{2}+14x-12=4\left(x-\frac{\sqrt{97}-7}{4}\right)\left(x-\frac{-\sqrt{97}-7}{4}\right)$$

Aromātai

$$4x^{2}+14x-12$$