Whakaoti i te -x^2+2x+3+(-4x+8)

$$- x ^ { 2 } + 2 x + 3 + ( - 4 x + 8 )$$

Aromātai

$$11-2x-x^{2}$$

Ngā Upane Otinga

Pahekotia te 2x me -4x, ka -2x.

$$-x^{2}-2x+3+8$$

Tāpirihia te 3 ki te 8, ka 11.

$$-x^{2}-2x+11$$

Tauwehe

$$-\left(x-\left(-2\sqrt{3}-1\right)\right)\left(x-\left(2\sqrt{3}-1\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 2x me -4x, ka -2x.

$$factor(-x^{2}-2x+3+8)$$

Tāpirihia te 3 ki te 8, ka 11.

$$factor(-x^{2}-2x+11)$$

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.

$$-x^{2}-2x+11=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 11}}{2\left(-1\right)}$$

Whakareatia 4 ki te 11.

$$x=\frac{-\left(-2\right)±\sqrt{4+44}}{2\left(-1\right)}$$

Tāpiri 4 ki te 44.

$$x=\frac{-\left(-2\right)±\sqrt{48}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 48.

$$x=\frac{-\left(-2\right)±4\sqrt{3}}{2\left(-1\right)}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±4\sqrt{3}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{2±4\sqrt{3}}{-2}$$

Nā, me whakaoti te whārite x=\frac{2±4\sqrt{3}}{-2} ina he tāpiri te ±. Tāpiri 2 ki te 4\sqrt{3}.

$$x=\frac{4\sqrt{3}+2}{-2}$$

Whakawehe 2+4\sqrt{3} ki te -2.

$$x=-2\sqrt{3}-1$$

Nā, me whakaoti te whārite x=\frac{2±4\sqrt{3}}{-2} ina he tango te ±. Tango 4\sqrt{3} mai i 2.

$$x=\frac{2-4\sqrt{3}}{-2}$$

Whakawehe 2-4\sqrt{3} ki te -2.

$$x=2\sqrt{3}-1$$

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

$$-x^{2}-2x+11=-\left(x-\left(-2\sqrt{3}-1\right)\right)\left(x-\left(2\sqrt{3}-1\right)\right)$$