Whakaoti i te 27x^2+11x-2

$$27 x ^ { 2 } + 11 x - 2$$

Tauwehe

$$27\left(x-\frac{-\sqrt{337}-11}{54}\right)\left(x-\frac{\sqrt{337}-11}{54}\right)$$

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.

$$27x^{2}+11x-2=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 27\left(-2\right)}}{2\times 27}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\times 27\left(-2\right)}}{2\times 27}$$

Whakareatia -4 ki te 27.

$$x=\frac{-11±\sqrt{121-108\left(-2\right)}}{2\times 27}$$

Whakareatia -108 ki te -2.

$$x=\frac{-11±\sqrt{121+216}}{2\times 27}$$

Tāpiri 121 ki te 216.

$$x=\frac{-11±\sqrt{337}}{2\times 27}$$

Whakareatia 2 ki te 27.

$$x=\frac{-11±\sqrt{337}}{54}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{337}}{54} ina he tāpiri te ±. Tāpiri -11 ki te \sqrt{337}.

$$x=\frac{\sqrt{337}-11}{54}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{337}}{54} ina he tango te ±. Tango \sqrt{337} mai i -11.

$$x=\frac{-\sqrt{337}-11}{54}$$

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{-11+\sqrt{337}}{54} mō te x_{1} me te \frac{-11-\sqrt{337}}{54} mō te x_{2}.

$$27x^{2}+11x-2=27\left(x-\frac{\sqrt{337}-11}{54}\right)\left(x-\frac{-\sqrt{337}-11}{54}\right)$$

Aromātai

$$27x^{2}+11x-2$$