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2x^{2}+x-1=0
Tangohia te 1 mai i ngā taha e rua.
a+b=1 ab=2\left(-1\right)=-2
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2x^{2}+ax+bx-1. 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(2x^{2}-x\right)+\left(2x-1\right)
Tuhia anō te 2x^{2}+x-1 hei \left(2x^{2}-x\right)+\left(2x-1\right).
x\left(2x-1\right)+2x-1
Whakatauwehea atu x i te 2x^{2}-x.
\left(2x-1\right)\left(x+1\right)
Whakatauwehea atu te kīanga pātahi 2x-1 mā te whakamahi i te āhuatanga tātai tohatoha.
x=\frac{1}{2} x=-1
Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te x+1=0.
2x^{2}+x=1
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.
2x^{2}+x-1=1-1
Me tango 1 mai i ngā taha e rua o te whārite.
2x^{2}+x-1=0
Mā te tango i te 1 i a ia ake anō ka toe ko te 0.
x=\frac{-1±\sqrt{1^{2}-4\times 2\left(-1\right)}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 1 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1±\sqrt{1-4\times 2\left(-1\right)}}{2\times 2}
Pūrua 1.
x=\frac{-1±\sqrt{1-8\left(-1\right)}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-1±\sqrt{1+8}}{2\times 2}
Whakareatia -8 ki te -1.
x=\frac{-1±\sqrt{9}}{2\times 2}
Tāpiri 1 ki te 8.
x=\frac{-1±3}{2\times 2}
Tuhia te pūtakerua o te 9.
x=\frac{-1±3}{4}
Whakareatia 2 ki te 2.
x=\frac{2}{4}
Nā, me whakaoti te whārite x=\frac{-1±3}{4} ina he tāpiri te ±. Tāpiri -1 ki te 3.
x=\frac{1}{2}
Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x=-\frac{4}{4}
Nā, me whakaoti te whārite x=\frac{-1±3}{4} ina he tango te ±. Tango 3 mai i -1.
x=-1
Whakawehe -4 ki te 4.
x=\frac{1}{2} x=-1
Kua oti te whārite te whakatau.
2x^{2}+x=1
Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.
\frac{2x^{2}+x}{2}=\frac{1}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}+\frac{1}{2}x=\frac{1}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}+\frac{1}{2}x+\left(\frac{1}{4}\right)^{2}=\frac{1}{2}+\left(\frac{1}{4}\right)^{2}
Whakawehea te \frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{4}. Nā, tāpiria te pūrua o te \frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{1}{2}+\frac{1}{16}
Pūruatia \frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{9}{16}
Tāpiri \frac{1}{2} ki te \frac{1}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
\left(x+\frac{1}{4}\right)^{2}=\frac{9}{16}
Tauwehea x^{2}+\frac{1}{2}x+\frac{1}{16}. 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}{4}\right)^{2}}=\sqrt{\frac{9}{16}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{1}{4}=\frac{3}{4} x+\frac{1}{4}=-\frac{3}{4}
Whakarūnātia.
x=\frac{1}{2} x=-1
Me tango \frac{1}{4} mai i ngā taha e rua o te whārite.