Whakaoti i te 3x^2+4x-8-2x^2+4x+2

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

Aromātai

$$x^{2}+8x-6$$

Ngā Upane Otinga

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

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

Pahekotia te 4x me 4x, ka 8x.

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

Tāpirihia te -8 ki te 2, ka -6.

$$x^{2}+8x-6$$

Tauwehe

$$\left(x-\left(-\sqrt{22}-4\right)\right)\left(x-\left(\sqrt{22}-4\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Pahekotia te 4x me 4x, ka 8x.

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

Tāpirihia te -8 ki te 2, ka -6.

$$factor(x^{2}+8x-6)$$

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.

$$x^{2}+8x-6=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-6\right)}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$x=\frac{-8±\sqrt{64+24}}{2}$$

Tāpiri 64 ki te 24.

$$x=\frac{-8±\sqrt{88}}{2}$$

Tuhia te pūtakerua o te 88.

$$x=\frac{-8±2\sqrt{22}}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{22}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{22}.

$$x=\frac{2\sqrt{22}-8}{2}$$

Whakawehe -8+2\sqrt{22} ki te 2.

$$x=\sqrt{22}-4$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{22}}{2} ina he tango te ±. Tango 2\sqrt{22} mai i -8.

$$x=\frac{-2\sqrt{22}-8}{2}$$

Whakawehe -8-2\sqrt{22} ki te 2.

$$x=-\sqrt{22}-4$$

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 -4+\sqrt{22} mō te x_{1} me te -4-\sqrt{22} mō te x_{2}.

$$x^{2}+8x-6=\left(x-\left(\sqrt{22}-4\right)\right)\left(x-\left(-\sqrt{22}-4\right)\right)$$