Whakaoti i te 3x^2-3x-225

$$3 x ^ { 2 } - 3 x - 225$$

Tauwehe

$$3\left(x-\frac{1-\sqrt{301}}{2}\right)\left(x-\frac{\sqrt{301}+1}{2}\right)$$

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.

$$3x^{2}-3x-225=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 3\left(-225\right)}}{2\times 3}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 3\left(-225\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-3\right)±\sqrt{9-12\left(-225\right)}}{2\times 3}$$

Whakareatia -12 ki te -225.

$$x=\frac{-\left(-3\right)±\sqrt{9+2700}}{2\times 3}$$

Tāpiri 9 ki te 2700.

$$x=\frac{-\left(-3\right)±\sqrt{2709}}{2\times 3}$$

Tuhia te pūtakerua o te 2709.

$$x=\frac{-\left(-3\right)±3\sqrt{301}}{2\times 3}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3\sqrt{301}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{3±3\sqrt{301}}{6}$$

Nā, me whakaoti te whārite x=\frac{3±3\sqrt{301}}{6} ina he tāpiri te ±. Tāpiri 3 ki te 3\sqrt{301}.

$$x=\frac{3\sqrt{301}+3}{6}$$

Whakawehe 3+3\sqrt{301} ki te 6.

$$x=\frac{\sqrt{301}+1}{2}$$

Nā, me whakaoti te whārite x=\frac{3±3\sqrt{301}}{6} ina he tango te ±. Tango 3\sqrt{301} mai i 3.

$$x=\frac{3-3\sqrt{301}}{6}$$

Whakawehe 3-3\sqrt{301} ki te 6.

$$x=\frac{1-\sqrt{301}}{2}$$

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{301}}{2} mō te x_{1} me te \frac{1-\sqrt{301}}{2} mō te x_{2}.

$$3x^{2}-3x-225=3\left(x-\frac{\sqrt{301}+1}{2}\right)\left(x-\frac{1-\sqrt{301}}{2}\right)$$

Aromātai

$$3\left(x^{2}-x-75\right)$$