Whakaoti mō x
x=-2
Graph
Tohaina
Kua tāruatia ki te papatopenga
a+b=4 ab=4
Hei whakaoti i te whārite, whakatauwehea te x^{2}+4x+4 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). 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\right)\left(x+2\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
\left(x+2\right)^{2}
Tuhia anōtia hei pūrua huarua.
x=-2
Hei kimi i te otinga whārite, whakaotia te x+2=0.
a+b=4 ab=1\times 4=4
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī 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.
x=-2
Hei kimi i te otinga whārite, whakaotia te x+2=0.
x^{2}+4x+4=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{-4±\sqrt{4^{2}-4\times 4}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
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}{2}
Tuhia te pūtakerua o te 0.
x=-2
Whakawehe -4 ki te 2.
\left(x+2\right)^{2}=0
Tauwehea x^{2}+4x+4. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+2\right)^{2}}=\sqrt{0}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+2=0 x+2=0
Whakarūnātia.
x=-2 x=-2
Me tango 2 mai i ngā taha e rua o te whārite.
x=-2
Kua oti te whārite te whakatau. He ōrite ngā whakatau.
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