Whakaoti i te {r}{-4x^2-48x}{+36}

$$\left. \begin{array} { r } { - 4 x ^ { 2 } - 48 x } \\ { + 36 } \end{array} \right.$$

Tauwehe

$$-4\left(x-\left(-3\sqrt{5}-6\right)\right)\left(x-\left(3\sqrt{5}-6\right)\right)$$

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.

$$-4x^{2}-48x+36=0$$

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.

$$x=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}-4\left(-4\right)\times 36}}{2\left(-4\right)}$$

Pūrua -48.

$$x=\frac{-\left(-48\right)±\sqrt{2304-4\left(-4\right)\times 36}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-\left(-48\right)±\sqrt{2304+16\times 36}}{2\left(-4\right)}$$

Whakareatia 16 ki te 36.

$$x=\frac{-\left(-48\right)±\sqrt{2304+576}}{2\left(-4\right)}$$

Tāpiri 2304 ki te 576.

$$x=\frac{-\left(-48\right)±\sqrt{2880}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 2880.

$$x=\frac{-\left(-48\right)±24\sqrt{5}}{2\left(-4\right)}$$

Ko te tauaro o -48 ko 48.

$$x=\frac{48±24\sqrt{5}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{48±24\sqrt{5}}{-8}$$

Nā, me whakaoti te whārite x=\frac{48±24\sqrt{5}}{-8} ina he tāpiri te ±. Tāpiri 48 ki te 24\sqrt{5}.

$$x=\frac{24\sqrt{5}+48}{-8}$$

Whakawehe 48+24\sqrt{5} ki te -8.

$$x=-3\sqrt{5}-6$$

Nā, me whakaoti te whārite x=\frac{48±24\sqrt{5}}{-8} ina he tango te ±. Tango 24\sqrt{5} mai i 48.

$$x=\frac{48-24\sqrt{5}}{-8}$$

Whakawehe 48-24\sqrt{5} ki te -8.

$$x=3\sqrt{5}-6$$

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 -6-3\sqrt{5} mō te x_{1} me te -6+3\sqrt{5} mō te x_{2}.

$$-4x^{2}-48x+36=-4\left(x-\left(-3\sqrt{5}-6\right)\right)\left(x-\left(3\sqrt{5}-6\right)\right)$$

Aromātai

$$36-48x-4x^{2}$$