Whakaoti i te (2x^2+7x+2)+(x+2)

$$( 2 x ^ { 2 } + 7 x + 2 ) + ( x + 2 )$$

Aromātai

$$2\left(x^{2}+4x+2\right)$$

Ngā Upane Otinga

Pahekotia te 7x me x, ka 8x.

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

Tāpirihia te 2 ki te 2, ka 4.

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

Tauwehe

$$2\left(x-\left(-\sqrt{2}-2\right)\right)\left(x-\left(\sqrt{2}-2\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 7x me x, ka 8x.

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

Tāpirihia te 2 ki te 2, ka 4.

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

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.

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

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2\times 4}}{2\times 2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 2\times 4}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-8±\sqrt{64-8\times 4}}{2\times 2}$$

Whakareatia -8 ki te 4.

$$x=\frac{-8±\sqrt{64-32}}{2\times 2}$$

Tāpiri 64 ki te -32.

$$x=\frac{-8±\sqrt{32}}{2\times 2}$$

Tuhia te pūtakerua o te 32.

$$x=\frac{-8±4\sqrt{2}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-8±4\sqrt{2}}{4}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{2}}{4} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{2}.

$$x=\frac{4\sqrt{2}-8}{4}$$

Whakawehe -8+4\sqrt{2} ki te 4.

$$x=\sqrt{2}-2$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{2}}{4} ina he tango te ±. Tango 4\sqrt{2} mai i -8.

$$x=\frac{-4\sqrt{2}-8}{4}$$

Whakawehe -8-4\sqrt{2} ki te 4.

$$x=-\sqrt{2}-2$$

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

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