Whakaoti i te 486+108x+6x^2

$$486 + 108 x + 6 x ^ { 2 }$$

Tauwehe

$$6\left(x+9\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(81+18x+x^{2}\right)$$

Whakaarohia te 81+18x+x^{2}. Whakamahia te tikanga tātai pūrua pā, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, ina a=x, ina b=9.

$$\left(x+9\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6\left(x+9\right)^{2}$$

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.

$$factor(6x^{2}+108x+486)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(6,108,486)=6$$

Tauwehea te 6.

$$6\left(x^{2}+18x+81\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 81.

$$\sqrt{81}=9$$

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.

$$6\left(x+9\right)^{2}$$

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.

$$6x^{2}+108x+486=0$$

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.

$$x=\frac{-108±\sqrt{108^{2}-4\times 6\times 486}}{2\times 6}$$

Pūrua 108.

$$x=\frac{-108±\sqrt{11664-4\times 6\times 486}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-108±\sqrt{11664-24\times 486}}{2\times 6}$$

Whakareatia -24 ki te 486.

$$x=\frac{-108±\sqrt{11664-11664}}{2\times 6}$$

Tāpiri 11664 ki te -11664.

$$x=\frac{-108±\sqrt{0}}{2\times 6}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-108±0}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-108±0}{12}$$

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 -9 mō te x_{1} me te -9 mō te x_{2}.

$$6x^{2}+108x+486=6\left(x-\left(-9\right)\right)\left(x-\left(-9\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$6x^{2}+108x+486=6\left(x+9\right)\left(x+9\right)$$

Aromātai

$$6\left(x+9\right)^{2}$$