Whakaoti i te x^2-4x^2+4+8x

$$x ^ { 2 } - 4 x ^ { 2 } + 4 + 8 x$$

Tauwehe

$$-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x^{2} me -4x^{2}, ka -3x^{2}.

$$factor(-3x^{2}+4+8x)$$

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.

$$-3x^{2}+8x+4=0$$

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.

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

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-8±\sqrt{64+12\times 4}}{2\left(-3\right)}$$

Whakareatia 12 ki te 4.

$$x=\frac{-8±\sqrt{64+48}}{2\left(-3\right)}$$

Tāpiri 64 ki te 48.

$$x=\frac{-8±\sqrt{112}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 112.

$$x=\frac{-8±4\sqrt{7}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-8±4\sqrt{7}}{-6}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{7}}{-6} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{7}.

$$x=\frac{4\sqrt{7}-8}{-6}$$

Whakawehe -8+4\sqrt{7} ki te -6.

$$x=\frac{4-2\sqrt{7}}{3}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{7}}{-6} ina he tango te ±. Tango 4\sqrt{7} mai i -8.

$$x=\frac{-4\sqrt{7}-8}{-6}$$

Whakawehe -8-4\sqrt{7} ki te -6.

$$x=\frac{2\sqrt{7}+4}{3}$$

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{4-2\sqrt{7}}{3} mō te x_{1} me te \frac{4+2\sqrt{7}}{3} mō te x_{2}.

$$-3x^{2}+8x+4=-3\left(x-\frac{4-2\sqrt{7}}{3}\right)\left(x-\frac{2\sqrt{7}+4}{3}\right)$$

Aromātai

$$4+8x-3x^{2}$$

Ngā Upane Otinga

Pahekotia te x^{2} me -4x^{2}, ka -3x^{2}.

$$-3x^{2}+4+8x$$