Whakaoti i te x^2+6x-3=

$$x ^ { 2 } + 6 x - 3 =$$

Tauwehe

$$\left(x-\left(-2\sqrt{3}-3\right)\right)\left(x-\left(2\sqrt{3}-3\right)\right)$$

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.

$$x^{2}+6x-3=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-3\right)}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-3\right)}}{2}$$

Whakareatia -4 ki te -3.

$$x=\frac{-6±\sqrt{36+12}}{2}$$

Tāpiri 36 ki te 12.

$$x=\frac{-6±\sqrt{48}}{2}$$

Tuhia te pūtakerua o te 48.

$$x=\frac{-6±4\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 4\sqrt{3}.

$$x=\frac{4\sqrt{3}-6}{2}$$

Whakawehe -6+4\sqrt{3} ki te 2.

$$x=2\sqrt{3}-3$$

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{2} ina he tango te ±. Tango 4\sqrt{3} mai i -6.

$$x=\frac{-4\sqrt{3}-6}{2}$$

Whakawehe -6-4\sqrt{3} ki te 2.

$$x=-2\sqrt{3}-3$$

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

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

Aromātai

$$x^{2}+6x-3$$