Whakaoti i te 3x^2+24x-44

$$3 x ^ { 2 } + 24 x - 44$$

Tauwehe

$$3\left(x-\left(-\frac{2\sqrt{69}}{3}-4\right)\right)\left(x-\left(\frac{2\sqrt{69}}{3}-4\right)\right)$$

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.

$$3x^{2}+24x-44=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}-4\times 3\left(-44\right)}}{2\times 3}$$

Pūrua 24.

$$x=\frac{-24±\sqrt{576-4\times 3\left(-44\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-24±\sqrt{576-12\left(-44\right)}}{2\times 3}$$

Whakareatia -12 ki te -44.

$$x=\frac{-24±\sqrt{576+528}}{2\times 3}$$

Tāpiri 576 ki te 528.

$$x=\frac{-24±\sqrt{1104}}{2\times 3}$$

Tuhia te pūtakerua o te 1104.

$$x=\frac{-24±4\sqrt{69}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-24±4\sqrt{69}}{6}$$

Nā, me whakaoti te whārite x=\frac{-24±4\sqrt{69}}{6} ina he tāpiri te ±. Tāpiri -24 ki te 4\sqrt{69}.

$$x=\frac{4\sqrt{69}-24}{6}$$

Whakawehe -24+4\sqrt{69} ki te 6.

$$x=\frac{2\sqrt{69}}{3}-4$$

Nā, me whakaoti te whārite x=\frac{-24±4\sqrt{69}}{6} ina he tango te ±. Tango 4\sqrt{69} mai i -24.

$$x=\frac{-4\sqrt{69}-24}{6}$$

Whakawehe -24-4\sqrt{69} ki te 6.

$$x=-\frac{2\sqrt{69}}{3}-4$$

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 -4+\frac{2\sqrt{69}}{3} mō te x_{1} me te -4-\frac{2\sqrt{69}}{3} mō te x_{2}.

$$3x^{2}+24x-44=3\left(x-\left(\frac{2\sqrt{69}}{3}-4\right)\right)\left(x-\left(-\frac{2\sqrt{69}}{3}-4\right)\right)$$

Aromātai

$$3x^{2}+24x-44$$