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a+b=4 ab=1\times 4=4
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,4 2,2
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 4.
1+4=5 2+2=4
Tātaihia te tapeke mō ia takirua.
a=2 b=2
Ko te otinga te takirua ka hoatu i te tapeke 4.
\left(x^{2}+2x\right)+\left(2x+4\right)
Tuhia anō te x^{2}+4x+4 hei \left(x^{2}+2x\right)+\left(2x+4\right).
x\left(x+2\right)+2\left(x+2\right)
Tauwehea te x i te tuatahi me te 2 i te rōpū tuarua.
\left(x+2\right)\left(x+2\right)
Whakatauwehea atu te kīanga pātahi x+2 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x+2\right)^{2}
Tuhia anōtia hei pūrua huarua.
factor(x^{2}+4x+4)
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{4}=2
Kimihia te pūtakerua o te kīanga tau autō, 4.
\left(x+2\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}+4x+4=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{-4±\sqrt{4^{2}-4\times 4}}{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{-4±\sqrt{16-4\times 4}}{2}
Pūrua 4.
x=\frac{-4±\sqrt{16-16}}{2}
Whakareatia -4 ki te 4.
x=\frac{-4±\sqrt{0}}{2}
Tāpiri 16 ki te -16.
x=\frac{-4±0}{2}
Tuhia te pūtakerua o te 0.
x^{2}+4x+4=\left(x-\left(-2\right)\right)\left(x-\left(-2\right)\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 -2 mō te x_{1} me te -2 mō te x_{2}.
x^{2}+4x+4=\left(x+2\right)\left(x+2\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.