Whakaoti i te 6x^2+11x-9

$$6 { x }^{ 2 } +11x-9$$

Tauwehe

$$6\left(x-\frac{-\sqrt{337}-11}{12}\right)\left(x-\frac{\sqrt{337}-11}{12}\right)$$

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.

$$6x^{2}+11x-9=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 6\left(-9\right)}}{2\times 6}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\times 6\left(-9\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-11±\sqrt{121-24\left(-9\right)}}{2\times 6}$$

Whakareatia -24 ki te -9.

$$x=\frac{-11±\sqrt{121+216}}{2\times 6}$$

Tāpiri 121 ki te 216.

$$x=\frac{-11±\sqrt{337}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-11±\sqrt{337}}{12}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{337}}{12} ina he tāpiri te ±. Tāpiri -11 ki te \sqrt{337}.

$$x=\frac{\sqrt{337}-11}{12}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{337}}{12} ina he tango te ±. Tango \sqrt{337} mai i -11.

$$x=\frac{-\sqrt{337}-11}{12}$$

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}}{12} mō te x_{1} me te \frac{-11-\sqrt{337}}{12} mō te x_{2}.

$$6x^{2}+11x-9=6\left(x-\frac{\sqrt{337}-11}{12}\right)\left(x-\frac{-\sqrt{337}-11}{12}\right)$$

Aromātai

$$6x^{2}+11x-9$$