Whakaoti i te 4x^2-3x-4

$$4 x ^ { 2 } - 3 x - 4$$

Tauwehe

$$4\left(x-\frac{3-\sqrt{73}}{8}\right)\left(x-\frac{\sqrt{73}+3}{8}\right)$$

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.

$$4x^{2}-3x-4=0$$

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.

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

Pūrua -3.

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

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-3\right)±\sqrt{9-16\left(-4\right)}}{2\times 4}$$

Whakareatia -16 ki te -4.

$$x=\frac{-\left(-3\right)±\sqrt{9+64}}{2\times 4}$$

Tāpiri 9 ki te 64.

$$x=\frac{-\left(-3\right)±\sqrt{73}}{2\times 4}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±\sqrt{73}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{3±\sqrt{73}}{8}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{73}}{8} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{73}.

$$x=\frac{\sqrt{73}+3}{8}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{73}}{8} ina he tango te ±. Tango \sqrt{73} mai i 3.

$$x=\frac{3-\sqrt{73}}{8}$$

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{3+\sqrt{73}}{8} mō te x_{1} me te \frac{3-\sqrt{73}}{8} mō te x_{2}.

$$4x^{2}-3x-4=4\left(x-\frac{\sqrt{73}+3}{8}\right)\left(x-\frac{3-\sqrt{73}}{8}\right)$$

Aromātai

$$4x^{2}-3x-4$$