Whakaoti i te 6x^2-2x-6

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

Tauwehe

$$6\left(x-\frac{1-\sqrt{37}}{6}\right)\left(x-\frac{\sqrt{37}+1}{6}\right)$$

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.

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

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.

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

Pūrua -2.

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

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-2\right)±\sqrt{4-24\left(-6\right)}}{2\times 6}$$

Whakareatia -24 ki te -6.

$$x=\frac{-\left(-2\right)±\sqrt{4+144}}{2\times 6}$$

Tāpiri 4 ki te 144.

$$x=\frac{-\left(-2\right)±\sqrt{148}}{2\times 6}$$

Tuhia te pūtakerua o te 148.

$$x=\frac{-\left(-2\right)±2\sqrt{37}}{2\times 6}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{37}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{2±2\sqrt{37}}{12}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{37}}{12} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{37}.

$$x=\frac{2\sqrt{37}+2}{12}$$

Whakawehe 2+2\sqrt{37} ki te 12.

$$x=\frac{\sqrt{37}+1}{6}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{37}}{12} ina he tango te ±. Tango 2\sqrt{37} mai i 2.

$$x=\frac{2-2\sqrt{37}}{12}$$

Whakawehe 2-2\sqrt{37} ki te 12.

$$x=\frac{1-\sqrt{37}}{6}$$

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 \frac{1+\sqrt{37}}{6} mō te x_{1} me te \frac{1-\sqrt{37}}{6} mō te x_{2}.

$$6x^{2}-2x-6=6\left(x-\frac{\sqrt{37}+1}{6}\right)\left(x-\frac{1-\sqrt{37}}{6}\right)$$

Aromātai

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