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a+b=-8 ab=1\times 16=16
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-16 -2,-8 -4,-4
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 16.
-1-16=-17 -2-8=-10 -4-4=-8
Tātaihia te tapeke mō ia takirua.
a=-4 b=-4
Ko te otinga te takirua ka hoatu i te tapeke -8.
\left(x^{2}-4x\right)+\left(-4x+16\right)
Tuhia anō te x^{2}-8x+16 hei \left(x^{2}-4x\right)+\left(-4x+16\right).
x\left(x-4\right)-4\left(x-4\right)
Tauwehea te x i te tuatahi me te -4 i te rōpū tuarua.
\left(x-4\right)\left(x-4\right)
Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x-4\right)^{2}
Tuhia anōtia hei pūrua huarua.
factor(x^{2}-8x+16)
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.
\sqrt{16}=4
Kimihia te pūtakerua o te kīanga tau autō, 16.
\left(x-4\right)^{2}
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.
x^{2}-8x+16=0
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.
x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 16}}{2}
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(-8\right)±\sqrt{64-4\times 16}}{2}
Pūrua -8.
x=\frac{-\left(-8\right)±\sqrt{64-64}}{2}
Whakareatia -4 ki te 16.
x=\frac{-\left(-8\right)±\sqrt{0}}{2}
Tāpiri 64 ki te -64.
x=\frac{-\left(-8\right)±0}{2}
Tuhia te pūtakerua o te 0.
x=\frac{8±0}{2}
Ko te tauaro o -8 ko 8.
x^{2}-8x+16=\left(x-4\right)\left(x-4\right)
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 4 mō te x_{1} me te 4 mō te x_{2}.