Whakaoti i te 3x^2-19x-18

$$3 { x }^{ 2 } -19x-18$$

Tauwehe

$$3\left(x-\frac{19-\sqrt{577}}{6}\right)\left(x-\frac{\sqrt{577}+19}{6}\right)$$

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.

$$3x^{2}-19x-18=0$$

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.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 3\left(-18\right)}}{2\times 3}$$

Pūrua -19.

$$x=\frac{-\left(-19\right)±\sqrt{361-4\times 3\left(-18\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-19\right)±\sqrt{361-12\left(-18\right)}}{2\times 3}$$

Whakareatia -12 ki te -18.

$$x=\frac{-\left(-19\right)±\sqrt{361+216}}{2\times 3}$$

Tāpiri 361 ki te 216.

$$x=\frac{-\left(-19\right)±\sqrt{577}}{2\times 3}$$

Ko te tauaro o -19 ko 19.

$$x=\frac{19±\sqrt{577}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{19±\sqrt{577}}{6}$$

Nā, me whakaoti te whārite x=\frac{19±\sqrt{577}}{6} ina he tāpiri te ±. Tāpiri 19 ki te \sqrt{577}.

$$x=\frac{\sqrt{577}+19}{6}$$

Nā, me whakaoti te whārite x=\frac{19±\sqrt{577}}{6} ina he tango te ±. Tango \sqrt{577} mai i 19.

$$x=\frac{19-\sqrt{577}}{6}$$

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 \frac{19+\sqrt{577}}{6} mō te x_{1} me te \frac{19-\sqrt{577}}{6} mō te x_{2}.

$$3x^{2}-19x-18=3\left(x-\frac{\sqrt{577}+19}{6}\right)\left(x-\frac{19-\sqrt{577}}{6}\right)$$

Aromātai

$$3x^{2}-19x-18$$