Whakaoti i te x^2+14x+22

$$x ^ { 2 } + 14 x + 22$$

Tauwehe

$$\left(x-\left(-3\sqrt{3}-7\right)\right)\left(x-\left(3\sqrt{3}-7\right)\right)$$

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.

$$x^{2}+14x+22=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 22}}{2}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 22}}{2}$$

Whakareatia -4 ki te 22.

$$x=\frac{-14±\sqrt{196-88}}{2}$$

Tāpiri 196 ki te -88.

$$x=\frac{-14±\sqrt{108}}{2}$$

Tuhia te pūtakerua o te 108.

$$x=\frac{-14±6\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -14 ki te 6\sqrt{3}.

$$x=\frac{6\sqrt{3}-14}{2}$$

Whakawehe -14+6\sqrt{3} ki te 2.

$$x=3\sqrt{3}-7$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{3}}{2} ina he tango te ±. Tango 6\sqrt{3} mai i -14.

$$x=\frac{-6\sqrt{3}-14}{2}$$

Whakawehe -14-6\sqrt{3} ki te 2.

$$x=-3\sqrt{3}-7$$

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 -7+3\sqrt{3} mō te x_{1} me te -7-3\sqrt{3} mō te x_{2}.

$$x^{2}+14x+22=\left(x-\left(3\sqrt{3}-7\right)\right)\left(x-\left(-3\sqrt{3}-7\right)\right)$$

Aromātai

$$x^{2}+14x+22$$