Whakaoti i te =x^2-14x+19

$$= x ^ { 2 } - 14 x + 19$$

Tauwehe

$$\left(x-\left(7-\sqrt{30}\right)\right)\left(x-\left(\sqrt{30}+7\right)\right)$$

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.

$$x^{2}-14x+19=0$$

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.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 19}}{2}$$

Pūrua -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 19}}{2}$$

Whakareatia -4 ki te 19.

$$x=\frac{-\left(-14\right)±\sqrt{196-76}}{2}$$

Tāpiri 196 ki te -76.

$$x=\frac{-\left(-14\right)±\sqrt{120}}{2}$$

Tuhia te pūtakerua o te 120.

$$x=\frac{-\left(-14\right)±2\sqrt{30}}{2}$$

Ko te tauaro o -14 ko 14.

$$x=\frac{14±2\sqrt{30}}{2}$$

Nā, me whakaoti te whārite x=\frac{14±2\sqrt{30}}{2} ina he tāpiri te ±. Tāpiri 14 ki te 2\sqrt{30}.

$$x=\frac{2\sqrt{30}+14}{2}$$

Whakawehe 14+2\sqrt{30} ki te 2.

$$x=\sqrt{30}+7$$

Nā, me whakaoti te whārite x=\frac{14±2\sqrt{30}}{2} ina he tango te ±. Tango 2\sqrt{30} mai i 14.

$$x=\frac{14-2\sqrt{30}}{2}$$

Whakawehe 14-2\sqrt{30} ki te 2.

$$x=7-\sqrt{30}$$

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+\sqrt{30} mō te x_{1} me te 7-\sqrt{30} mō te x_{2}.

$$x^{2}-14x+19=\left(x-\left(\sqrt{30}+7\right)\right)\left(x-\left(7-\sqrt{30}\right)\right)$$

Aromātai

$$x^{2}-14x+19$$