Whakaoti i te -9x^2+18x+68=

$$- 9 x ^ { 2 } + 18 x + 68 =$$

Tauwehe

$$-9\left(x-\left(-\frac{\sqrt{77}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{77}}{3}+1\right)\right)$$

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.

$$-9x^{2}+18x+68=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-9\right)\times 68}}{2\left(-9\right)}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-9\right)\times 68}}{2\left(-9\right)}$$

Whakareatia -4 ki te -9.

$$x=\frac{-18±\sqrt{324+36\times 68}}{2\left(-9\right)}$$

Whakareatia 36 ki te 68.

$$x=\frac{-18±\sqrt{324+2448}}{2\left(-9\right)}$$

Tāpiri 324 ki te 2448.

$$x=\frac{-18±\sqrt{2772}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 2772.

$$x=\frac{-18±6\sqrt{77}}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$x=\frac{-18±6\sqrt{77}}{-18}$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{77}}{-18} ina he tāpiri te ±. Tāpiri -18 ki te 6\sqrt{77}.

$$x=\frac{6\sqrt{77}-18}{-18}$$

Whakawehe -18+6\sqrt{77} ki te -18.

$$x=-\frac{\sqrt{77}}{3}+1$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{77}}{-18} ina he tango te ±. Tango 6\sqrt{77} mai i -18.

$$x=\frac{-6\sqrt{77}-18}{-18}$$

Whakawehe -18-6\sqrt{77} ki te -18.

$$x=\frac{\sqrt{77}}{3}+1$$

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 1-\frac{\sqrt{77}}{3} mō te x_{1} me te 1+\frac{\sqrt{77}}{3} mō te x_{2}.

$$-9x^{2}+18x+68=-9\left(x-\left(-\frac{\sqrt{77}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{77}}{3}+1\right)\right)$$

Aromātai

$$68+18x-9x^{2}$$