Whakaoti i te 11x^2+9-4x-8x^2-15x

$$11 x ^ { 2 } + 9 - 4 x - 8 x ^ { 2 } - 15 x$$

Aromātai

$$3x^{2}-19x+9$$

Ngā Upane Otinga

Pahekotia te 11x^{2} me -8x^{2}, ka 3x^{2}.

$$3x^{2}+9-4x-15x$$

Pahekotia te -4x me -15x, ka -19x.

$$3x^{2}+9-19x$$

Tauwehe

$$3\left(x-\frac{19-\sqrt{253}}{6}\right)\left(x-\frac{\sqrt{253}+19}{6}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 11x^{2} me -8x^{2}, ka 3x^{2}.

$$factor(3x^{2}+9-4x-15x)$$

Pahekotia te -4x me -15x, ka -19x.

$$factor(3x^{2}+9-19x)$$

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.

$$3x^{2}-19x+9=0$$

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.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 3\times 9}}{2\times 3}$$

Pūrua -19.

$$x=\frac{-\left(-19\right)±\sqrt{361-4\times 3\times 9}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-19\right)±\sqrt{361-12\times 9}}{2\times 3}$$

Whakareatia -12 ki te 9.

$$x=\frac{-\left(-19\right)±\sqrt{361-108}}{2\times 3}$$

Tāpiri 361 ki te -108.

$$x=\frac{-\left(-19\right)±\sqrt{253}}{2\times 3}$$

Ko te tauaro o -19 ko 19.

$$x=\frac{19±\sqrt{253}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{19±\sqrt{253}}{6}$$

Nā, me whakaoti te whārite x=\frac{19±\sqrt{253}}{6} ina he tāpiri te ±. Tāpiri 19 ki te \sqrt{253}.

$$x=\frac{\sqrt{253}+19}{6}$$

Nā, me whakaoti te whārite x=\frac{19±\sqrt{253}}{6} ina he tango te ±. Tango \sqrt{253} mai i 19.

$$x=\frac{19-\sqrt{253}}{6}$$

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{253}}{6} mō te x_{1} me te \frac{19-\sqrt{253}}{6} mō te x_{2}.

$$3x^{2}-19x+9=3\left(x-\frac{\sqrt{253}+19}{6}\right)\left(x-\frac{19-\sqrt{253}}{6}\right)$$