Whakaoti i te 6x^2+4x-24

$$6 { x }^{ 2 } +4x-24$$

Tauwehe

$$6\left(x-\frac{-\sqrt{37}-1}{3}\right)\left(x-\frac{\sqrt{37}-1}{3}\right)$$

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.

$$6x^{2}+4x-24=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\times 6\left(-24\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-4±\sqrt{16-24\left(-24\right)}}{2\times 6}$$

Whakareatia -24 ki te -24.

$$x=\frac{-4±\sqrt{16+576}}{2\times 6}$$

Tāpiri 16 ki te 576.

$$x=\frac{-4±\sqrt{592}}{2\times 6}$$

Tuhia te pūtakerua o te 592.

$$x=\frac{-4±4\sqrt{37}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-4±4\sqrt{37}}{12}$$

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{37}}{12} ina he tāpiri te ±. Tāpiri -4 ki te 4\sqrt{37}.

$$x=\frac{4\sqrt{37}-4}{12}$$

Whakawehe -4+4\sqrt{37} ki te 12.

$$x=\frac{\sqrt{37}-1}{3}$$

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{37}}{12} ina he tango te ±. Tango 4\sqrt{37} mai i -4.

$$x=\frac{-4\sqrt{37}-4}{12}$$

Whakawehe -4-4\sqrt{37} ki te 12.

$$x=\frac{-\sqrt{37}-1}{3}$$

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{-1+\sqrt{37}}{3} mō te x_{1} me te \frac{-1-\sqrt{37}}{3} mō te x_{2}.

$$6x^{2}+4x-24=6\left(x-\frac{\sqrt{37}-1}{3}\right)\left(x-\frac{-\sqrt{37}-1}{3}\right)$$

Aromātai

$$6x^{2}+4x-24$$