Whakaoti i te 13x^2-66x+36

$$13 x ^ { 2 } - 66 x + 36$$

Tauwehe

$$13\left(x-\frac{33-3\sqrt{69}}{13}\right)\left(x-\frac{3\sqrt{69}+33}{13}\right)$$

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.

$$13x^{2}-66x+36=0$$

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.

$$x=\frac{-\left(-66\right)±\sqrt{\left(-66\right)^{2}-4\times 13\times 36}}{2\times 13}$$

Pūrua -66.

$$x=\frac{-\left(-66\right)±\sqrt{4356-4\times 13\times 36}}{2\times 13}$$

Whakareatia -4 ki te 13.

$$x=\frac{-\left(-66\right)±\sqrt{4356-52\times 36}}{2\times 13}$$

Whakareatia -52 ki te 36.

$$x=\frac{-\left(-66\right)±\sqrt{4356-1872}}{2\times 13}$$

Tāpiri 4356 ki te -1872.

$$x=\frac{-\left(-66\right)±\sqrt{2484}}{2\times 13}$$

Tuhia te pūtakerua o te 2484.

$$x=\frac{-\left(-66\right)±6\sqrt{69}}{2\times 13}$$

Ko te tauaro o -66 ko 66.

$$x=\frac{66±6\sqrt{69}}{2\times 13}$$

Whakareatia 2 ki te 13.

$$x=\frac{66±6\sqrt{69}}{26}$$

Nā, me whakaoti te whārite x=\frac{66±6\sqrt{69}}{26} ina he tāpiri te ±. Tāpiri 66 ki te 6\sqrt{69}.

$$x=\frac{6\sqrt{69}+66}{26}$$

Whakawehe 66+6\sqrt{69} ki te 26.

$$x=\frac{3\sqrt{69}+33}{13}$$

Nā, me whakaoti te whārite x=\frac{66±6\sqrt{69}}{26} ina he tango te ±. Tango 6\sqrt{69} mai i 66.

$$x=\frac{66-6\sqrt{69}}{26}$$

Whakawehe 66-6\sqrt{69} ki te 26.

$$x=\frac{33-3\sqrt{69}}{13}$$

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{33+3\sqrt{69}}{13} mō te x_{1} me te \frac{33-3\sqrt{69}}{13} mō te x_{2}.

$$13x^{2}-66x+36=13\left(x-\frac{3\sqrt{69}+33}{13}\right)\left(x-\frac{33-3\sqrt{69}}{13}\right)$$

Aromātai

$$13x^{2}-66x+36$$