Whakaoti i te 18x^2+24x+7

$$18 x ^ { 2 } + 24 x + 7$$

Tauwehe

$$18\left(x-\left(-\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)\left(x-\left(\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)$$

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.

$$18x^{2}+24x+7=0$$

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.

$$x=\frac{-24±\sqrt{24^{2}-4\times 18\times 7}}{2\times 18}$$

Pūrua 24.

$$x=\frac{-24±\sqrt{576-4\times 18\times 7}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$x=\frac{-24±\sqrt{576-72\times 7}}{2\times 18}$$

Whakareatia -72 ki te 7.

$$x=\frac{-24±\sqrt{576-504}}{2\times 18}$$

Tāpiri 576 ki te -504.

$$x=\frac{-24±\sqrt{72}}{2\times 18}$$

Tuhia te pūtakerua o te 72.

$$x=\frac{-24±6\sqrt{2}}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{-24±6\sqrt{2}}{36}$$

Nā, me whakaoti te whārite x=\frac{-24±6\sqrt{2}}{36} ina he tāpiri te ±. Tāpiri -24 ki te 6\sqrt{2}.

$$x=\frac{6\sqrt{2}-24}{36}$$

Whakawehe -24+6\sqrt{2} ki te 36.

$$x=\frac{\sqrt{2}}{6}-\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{-24±6\sqrt{2}}{36} ina he tango te ±. Tango 6\sqrt{2} mai i -24.

$$x=\frac{-6\sqrt{2}-24}{36}$$

Whakawehe -24-6\sqrt{2} ki te 36.

$$x=-\frac{\sqrt{2}}{6}-\frac{2}{3}$$

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{2}{3}+\frac{\sqrt{2}}{6} mō te x_{1} me te -\frac{2}{3}-\frac{\sqrt{2}}{6} mō te x_{2}.

$$18x^{2}+24x+7=18\left(x-\left(\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)\left(x-\left(-\frac{\sqrt{2}}{6}-\frac{2}{3}\right)\right)$$

Aromātai

$$18x^{2}+24x+7$$