Whakaoti mō x
x=-2
x=1
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}+x=1\times 2
Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.
x^{2}+x=2
Whakareatia te 1 ki te 2, ka 2.
x^{2}+x-2=0
Tangohia te 2 mai i ngā taha e rua.
a+b=1 ab=-2
Hei whakaoti i te whārite, whakatauwehea te x^{2}+x-2 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.
a=-1 b=2
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x-1\right)\left(x+2\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=1 x=-2
Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+2=0.
x^{2}+x=1\times 2
Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.
x^{2}+x=2
Whakareatia te 1 ki te 2, ka 2.
x^{2}+x-2=0
Tangohia te 2 mai i ngā taha e rua.
a+b=1 ab=1\left(-2\right)=-2
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-1 b=2
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}-x\right)+\left(2x-2\right)
Tuhia anō te x^{2}+x-2 hei \left(x^{2}-x\right)+\left(2x-2\right).
x\left(x-1\right)+2\left(x-1\right)
Tauwehea te x i te tuatahi me te 2 i te rōpū tuarua.
\left(x-1\right)\left(x+2\right)
Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.
x=1 x=-2
Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+2=0.
x^{2}+x=1\times 2
Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.
x^{2}+x=2
Whakareatia te 1 ki te 2, ka 2.
x^{2}+x-2=0
Tangohia te 2 mai i ngā taha e rua.
x=\frac{-1±\sqrt{1^{2}-4\left(-2\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1±\sqrt{1-4\left(-2\right)}}{2}
Pūrua 1.
x=\frac{-1±\sqrt{1+8}}{2}
Whakareatia -4 ki te -2.
x=\frac{-1±\sqrt{9}}{2}
Tāpiri 1 ki te 8.
x=\frac{-1±3}{2}
Tuhia te pūtakerua o te 9.
x=\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{-1±3}{2} ina he tāpiri te ±. Tāpiri -1 ki te 3.
x=1
Whakawehe 2 ki te 2.
x=-\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{-1±3}{2} ina he tango te ±. Tango 3 mai i -1.
x=-2
Whakawehe -4 ki te 2.
x=1 x=-2
Kua oti te whārite te whakatau.
x^{2}+x=1\times 2
Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.
x^{2}+x=2
Whakareatia te 1 ki te 2, ka 2.
x^{2}+x+\left(\frac{1}{2}\right)^{2}=2+\left(\frac{1}{2}\right)^{2}
Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+x+\frac{1}{4}=2+\frac{1}{4}
Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+x+\frac{1}{4}=\frac{9}{4}
Tāpiri 2 ki te \frac{1}{4}.
\left(x+\frac{1}{2}\right)^{2}=\frac{9}{4}
Tauwehea x^{2}+x+\frac{1}{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+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{1}{2}=\frac{3}{2} x+\frac{1}{2}=-\frac{3}{2}
Whakarūnātia.
x=1 x=-2
Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.
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