Whakaoti i te 27x^2+18x+1=

$$27 x ^ { 2 } + 18 x + 1 =$$

Tauwehe

$$27\left(x-\left(-\frac{\sqrt{6}}{9}-\frac{1}{3}\right)\right)\left(x-\left(\frac{\sqrt{6}}{9}-\frac{1}{3}\right)\right)$$

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.

$$27x^{2}+18x+1=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 27}}{2\times 27}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 27}}{2\times 27}$$

Whakareatia -4 ki te 27.

$$x=\frac{-18±\sqrt{324-108}}{2\times 27}$$

Tāpiri 324 ki te -108.

$$x=\frac{-18±\sqrt{216}}{2\times 27}$$

Tuhia te pūtakerua o te 216.

$$x=\frac{-18±6\sqrt{6}}{2\times 27}$$

Whakareatia 2 ki te 27.

$$x=\frac{-18±6\sqrt{6}}{54}$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{6}}{54} ina he tāpiri te ±. Tāpiri -18 ki te 6\sqrt{6}.

$$x=\frac{6\sqrt{6}-18}{54}$$

Whakawehe -18+6\sqrt{6} ki te 54.

$$x=\frac{\sqrt{6}}{9}-\frac{1}{3}$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{6}}{54} ina he tango te ±. Tango 6\sqrt{6} mai i -18.

$$x=\frac{-6\sqrt{6}-18}{54}$$

Whakawehe -18-6\sqrt{6} ki te 54.

$$x=-\frac{\sqrt{6}}{9}-\frac{1}{3}$$

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}{3}+\frac{\sqrt{6}}{9} mō te x_{1} me te -\frac{1}{3}-\frac{\sqrt{6}}{9} mō te x_{2}.

$$27x^{2}+18x+1=27\left(x-\left(\frac{\sqrt{6}}{9}-\frac{1}{3}\right)\right)\left(x-\left(-\frac{\sqrt{6}}{9}-\frac{1}{3}\right)\right)$$

Aromātai

$$27x^{2}+18x+1$$