Whakaoti i te 4x^2+12x-5

$$4 x ^ { 2 } + 12 x - 5$$

Tauwehe

$$4\left(x-\frac{-\sqrt{14}-3}{2}\right)\left(x-\frac{\sqrt{14}-3}{2}\right)$$

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.

$$4x^{2}+12x-5=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 4\left(-5\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-12±\sqrt{144-16\left(-5\right)}}{2\times 4}$$

Whakareatia -16 ki te -5.

$$x=\frac{-12±\sqrt{144+80}}{2\times 4}$$

Tāpiri 144 ki te 80.

$$x=\frac{-12±\sqrt{224}}{2\times 4}$$

Tuhia te pūtakerua o te 224.

$$x=\frac{-12±4\sqrt{14}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-12±4\sqrt{14}}{8}$$

Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{14}}{8} ina he tāpiri te ±. Tāpiri -12 ki te 4\sqrt{14}.

$$x=\frac{4\sqrt{14}-12}{8}$$

Whakawehe -12+4\sqrt{14} ki te 8.

$$x=\frac{\sqrt{14}-3}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±4\sqrt{14}}{8} ina he tango te ±. Tango 4\sqrt{14} mai i -12.

$$x=\frac{-4\sqrt{14}-12}{8}$$

Whakawehe -12-4\sqrt{14} ki te 8.

$$x=\frac{-\sqrt{14}-3}{2}$$

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{-3+\sqrt{14}}{2} mō te x_{1} me te \frac{-3-\sqrt{14}}{2} mō te x_{2}.

$$4x^{2}+12x-5=4\left(x-\frac{\sqrt{14}-3}{2}\right)\left(x-\frac{-\sqrt{14}-3}{2}\right)$$

Aromātai

$$4x^{2}+12x-5$$