Whakaoti i te 2x^2+3x+17x+2

$$2 x ^ { 2 } + 3 x + 17 x + 2$$

Tauwehe

$$2\left(x-\left(-2\sqrt{6}-5\right)\right)\left(x-\left(2\sqrt{6}-5\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 3x me 17x, ka 20x.

$$factor(2x^{2}+20x+2)$$

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.

$$2x^{2}+20x+2=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 2\times 2}}{2\times 2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 2\times 2}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-20±\sqrt{400-8\times 2}}{2\times 2}$$

Whakareatia -8 ki te 2.

$$x=\frac{-20±\sqrt{400-16}}{2\times 2}$$

Tāpiri 400 ki te -16.

$$x=\frac{-20±\sqrt{384}}{2\times 2}$$

Tuhia te pūtakerua o te 384.

$$x=\frac{-20±8\sqrt{6}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-20±8\sqrt{6}}{4}$$

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{6}}{4} ina he tāpiri te ±. Tāpiri -20 ki te 8\sqrt{6}.

$$x=\frac{8\sqrt{6}-20}{4}$$

Whakawehe -20+8\sqrt{6} ki te 4.

$$x=2\sqrt{6}-5$$

Nā, me whakaoti te whārite x=\frac{-20±8\sqrt{6}}{4} ina he tango te ±. Tango 8\sqrt{6} mai i -20.

$$x=\frac{-8\sqrt{6}-20}{4}$$

Whakawehe -20-8\sqrt{6} ki te 4.

$$x=-2\sqrt{6}-5$$

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 -5+2\sqrt{6} mō te x_{1} me te -5-2\sqrt{6} mō te x_{2}.

$$2x^{2}+20x+2=2\left(x-\left(2\sqrt{6}-5\right)\right)\left(x-\left(-2\sqrt{6}-5\right)\right)$$

Aromātai

$$2\left(x^{2}+10x+1\right)$$

Ngā Upane Otinga

Pahekotia te 3x me 17x, ka 20x.

$$2x^{2}+20x+2$$