Whakaoti i te 128-32x+2x^2

$$128 - 32 x + 2 x ^ { 2 }$$

Tauwehe

$$2\left(x-8\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(64-16x+x^{2}\right)$$

Whakaarohia te 64-16x+x^{2}. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=x, ina b=8.

$$\left(x-8\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-8\right)^{2}$$

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(2x^{2}-32x+128)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(2,-32,128)=2$$

Tauwehea te 2.

$$2\left(x^{2}-16x+64\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 64.

$$\sqrt{64}=8$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

$$2\left(x-8\right)^{2}$$

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.

$$2x^{2}-32x+128=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 2\times 128}}{2\times 2}$$

Pūrua -32.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\times 2\times 128}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-32\right)±\sqrt{1024-8\times 128}}{2\times 2}$$

Whakareatia -8 ki te 128.

$$x=\frac{-\left(-32\right)±\sqrt{1024-1024}}{2\times 2}$$

Tāpiri 1024 ki te -1024.

$$x=\frac{-\left(-32\right)±\sqrt{0}}{2\times 2}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-\left(-32\right)±0}{2\times 2}$$

Ko te tauaro o -32 ko 32.

$$x=\frac{32±0}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{32±0}{4}$$

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 8 mō te x_{1} me te 8 mō te x_{2}.

$$2x^{2}-32x+128=2\left(x-8\right)\left(x-8\right)$$

Aromātai

$$2\left(x-8\right)^{2}$$