Whakaoti i te 14x-x^2-4

$$14 x - x ^ { 2 } - 4$$

Tauwehe

$$-\left(x-\left(7-3\sqrt{5}\right)\right)\left(x-\left(3\sqrt{5}+7\right)\right)$$

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.

$$-x^{2}+14x-4=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-1\right)\left(-4\right)}}{2\left(-1\right)}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\left(-1\right)\left(-4\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-14±\sqrt{196+4\left(-4\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -4.

$$x=\frac{-14±\sqrt{196-16}}{2\left(-1\right)}$$

Tāpiri 196 ki te -16.

$$x=\frac{-14±\sqrt{180}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 180.

$$x=\frac{-14±6\sqrt{5}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-14±6\sqrt{5}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{5}}{-2} ina he tāpiri te ±. Tāpiri -14 ki te 6\sqrt{5}.

$$x=\frac{6\sqrt{5}-14}{-2}$$

Whakawehe -14+6\sqrt{5} ki te -2.

$$x=7-3\sqrt{5}$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{5}}{-2} ina he tango te ±. Tango 6\sqrt{5} mai i -14.

$$x=\frac{-6\sqrt{5}-14}{-2}$$

Whakawehe -14-6\sqrt{5} ki te -2.

$$x=3\sqrt{5}+7$$

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{5} mō te x_{1} me te 7+3\sqrt{5} mō te x_{2}.

$$-x^{2}+14x-4=-\left(x-\left(7-3\sqrt{5}\right)\right)\left(x-\left(3\sqrt{5}+7\right)\right)$$

Aromātai

$$-x^{2}+14x-4$$