Whakaoti i te 8x^2+16x+4

$$8 x ^ { 2 } + 16 x + 4$$

Tauwehe

$$8\left(x-\left(-\frac{\sqrt{2}}{2}-1\right)\right)\left(x-\left(\frac{\sqrt{2}}{2}-1\right)\right)$$

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.

$$8x^{2}+16x+4=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\times 8\times 4}}{2\times 8}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\times 8\times 4}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-16±\sqrt{256-32\times 4}}{2\times 8}$$

Whakareatia -32 ki te 4.

$$x=\frac{-16±\sqrt{256-128}}{2\times 8}$$

Tāpiri 256 ki te -128.

$$x=\frac{-16±\sqrt{128}}{2\times 8}$$

Tuhia te pūtakerua o te 128.

$$x=\frac{-16±8\sqrt{2}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{-16±8\sqrt{2}}{16}$$

Nā, me whakaoti te whārite x=\frac{-16±8\sqrt{2}}{16} ina he tāpiri te ±. Tāpiri -16 ki te 8\sqrt{2}.

$$x=\frac{8\sqrt{2}-16}{16}$$

Whakawehe -16+8\sqrt{2} ki te 16.

$$x=\frac{\sqrt{2}}{2}-1$$

Nā, me whakaoti te whārite x=\frac{-16±8\sqrt{2}}{16} ina he tango te ±. Tango 8\sqrt{2} mai i -16.

$$x=\frac{-8\sqrt{2}-16}{16}$$

Whakawehe -16-8\sqrt{2} ki te 16.

$$x=-\frac{\sqrt{2}}{2}-1$$

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

$$8x^{2}+16x+4=8\left(x-\left(\frac{\sqrt{2}}{2}-1\right)\right)\left(x-\left(-\frac{\sqrt{2}}{2}-1\right)\right)$$

Aromātai

$$8x^{2}+16x+4$$