Whakaoti i te x^2-6x-30

$${ x }^{ 2 } -6x-30$$

Tauwehe

$$\left(x-\left(3-\sqrt{39}\right)\right)\left(x-\left(\sqrt{39}+3\right)\right)$$

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.

$$x^{2}-6x-30=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-30\right)}}{2}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-30\right)}}{2}$$

Whakareatia -4 ki te -30.

$$x=\frac{-\left(-6\right)±\sqrt{36+120}}{2}$$

Tāpiri 36 ki te 120.

$$x=\frac{-\left(-6\right)±\sqrt{156}}{2}$$

Tuhia te pūtakerua o te 156.

$$x=\frac{-\left(-6\right)±2\sqrt{39}}{2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{39}}{2}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{39}}{2} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{39}.

$$x=\frac{2\sqrt{39}+6}{2}$$

Whakawehe 6+2\sqrt{39} ki te 2.

$$x=\sqrt{39}+3$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{39}}{2} ina he tango te ±. Tango 2\sqrt{39} mai i 6.

$$x=\frac{6-2\sqrt{39}}{2}$$

Whakawehe 6-2\sqrt{39} ki te 2.

$$x=3-\sqrt{39}$$

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 3+\sqrt{39} mō te x_{1} me te 3-\sqrt{39} mō te x_{2}.

$$x^{2}-6x-30=\left(x-\left(\sqrt{39}+3\right)\right)\left(x-\left(3-\sqrt{39}\right)\right)$$

Aromātai

$$x^{2}-6x-30$$