Whakaoti i te x^2+12x-11

$$x ^ { 2 } + 12 x - 11$$

Tauwehe

$$\left(x-\left(-\sqrt{47}-6\right)\right)\left(x-\left(\sqrt{47}-6\right)\right)$$

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.

$$x^{2}+12x-11=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-11\right)}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-11\right)}}{2}$$

Whakareatia -4 ki te -11.

$$x=\frac{-12±\sqrt{144+44}}{2}$$

Tāpiri 144 ki te 44.

$$x=\frac{-12±\sqrt{188}}{2}$$

Tuhia te pūtakerua o te 188.

$$x=\frac{-12±2\sqrt{47}}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{47}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{47}.

$$x=\frac{2\sqrt{47}-12}{2}$$

Whakawehe -12+2\sqrt{47} ki te 2.

$$x=\sqrt{47}-6$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{47}}{2} ina he tango te ±. Tango 2\sqrt{47} mai i -12.

$$x=\frac{-2\sqrt{47}-12}{2}$$

Whakawehe -12-2\sqrt{47} ki te 2.

$$x=-\sqrt{47}-6$$

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+\sqrt{47} mō te x_{1} me te -6-\sqrt{47} mō te x_{2}.

$$x^{2}+12x-11=\left(x-\left(\sqrt{47}-6\right)\right)\left(x-\left(-\sqrt{47}-6\right)\right)$$

Aromātai

$$x^{2}+12x-11$$