Whakaoti i te {r}{54x^2+863x}{-432}

$$\left. \begin{array} { r } { 54 x ^ { 2 } + 863 x } \\ { - 432 } \end{array} \right.$$

Tauwehe

$$54\left(x-\frac{-\sqrt{838081}-863}{108}\right)\left(x-\frac{\sqrt{838081}-863}{108}\right)$$

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.

$$54x^{2}+863x-432=0$$

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.

$$x=\frac{-863±\sqrt{863^{2}-4\times 54\left(-432\right)}}{2\times 54}$$

Pūrua 863.

$$x=\frac{-863±\sqrt{744769-4\times 54\left(-432\right)}}{2\times 54}$$

Whakareatia -4 ki te 54.

$$x=\frac{-863±\sqrt{744769-216\left(-432\right)}}{2\times 54}$$

Whakareatia -216 ki te -432.

$$x=\frac{-863±\sqrt{744769+93312}}{2\times 54}$$

Tāpiri 744769 ki te 93312.

$$x=\frac{-863±\sqrt{838081}}{2\times 54}$$

Whakareatia 2 ki te 54.

$$x=\frac{-863±\sqrt{838081}}{108}$$

Nā, me whakaoti te whārite x=\frac{-863±\sqrt{838081}}{108} ina he tāpiri te ±. Tāpiri -863 ki te \sqrt{838081}.

$$x=\frac{\sqrt{838081}-863}{108}$$

Nā, me whakaoti te whārite x=\frac{-863±\sqrt{838081}}{108} ina he tango te ±. Tango \sqrt{838081} mai i -863.

$$x=\frac{-\sqrt{838081}-863}{108}$$

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{-863+\sqrt{838081}}{108} mō te x_{1} me te \frac{-863-\sqrt{838081}}{108} mō te x_{2}.

$$54x^{2}+863x-432=54\left(x-\frac{\sqrt{838081}-863}{108}\right)\left(x-\frac{-\sqrt{838081}-863}{108}\right)$$

Aromātai

$$54x^{2}+863x-432$$