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a+b=5 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=1 b=4
Ko te otinga te takirua ka hoatu i te tapeke 5.
\left(x^{2}+x\right)+\left(4x+4\right)
Tuhia anō te x^{2}+5x+4 hei \left(x^{2}+x\right)+\left(4x+4\right).
x\left(x+1\right)+4\left(x+1\right)
Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.
\left(x+1\right)\left(x+4\right)
Whakatauwehea atu te kīanga pātahi x+1 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}+5x+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{-5±\sqrt{5^{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{-5±\sqrt{25-4\times 4}}{2}
Pūrua 5.
x=\frac{-5±\sqrt{25-16}}{2}
Whakareatia -4 ki te 4.
x=\frac{-5±\sqrt{9}}{2}
Tāpiri 25 ki te -16.
x=\frac{-5±3}{2}
Tuhia te pūtakerua o te 9.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{-5±3}{2} ina he tāpiri te ±. Tāpiri -5 ki te 3.
x=-1
Whakawehe -2 ki te 2.
x=-\frac{8}{2}
Nā, me whakaoti te whārite x=\frac{-5±3}{2} ina he tango te ±. Tango 3 mai i -5.
x=-4
Whakawehe -8 ki te 2.
x^{2}+5x+4=\left(x-\left(-1\right)\right)\left(x-\left(-4\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 -1 mō te x_{1} me te -4 mō te x_{2}.
x^{2}+5x+4=\left(x+1\right)\left(x+4\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.