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x-1=2x\left(-x+2\right)-x+2
Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+2.
x-1=-2x^{2}+4x-x+2
Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te -x+2.
x-1=-2x^{2}+3x+2
Pahekotia te 4x me -x, ka 3x.
x-1+2x^{2}=3x+2
Me tāpiri te 2x^{2} ki ngā taha e rua.
x-1+2x^{2}-3x=2
Tangohia te 3x mai i ngā taha e rua.
-2x-1+2x^{2}=2
Pahekotia te x me -3x, ka -2x.
-2x-1+2x^{2}-2=0
Tangohia te 2 mai i ngā taha e rua.
-2x-3+2x^{2}=0
Tangohia te 2 i te -1, ka -3.
2x^{2}-2x-3=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{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\left(-3\right)}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -2 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\times 2\left(-3\right)}}{2\times 2}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4-8\left(-3\right)}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-\left(-2\right)±\sqrt{4+24}}{2\times 2}
Whakareatia -8 ki te -3.
x=\frac{-\left(-2\right)±\sqrt{28}}{2\times 2}
Tāpiri 4 ki te 24.
x=\frac{-\left(-2\right)±2\sqrt{7}}{2\times 2}
Tuhia te pūtakerua o te 28.
x=\frac{2±2\sqrt{7}}{2\times 2}
Ko te tauaro o -2 ko 2.
x=\frac{2±2\sqrt{7}}{4}
Whakareatia 2 ki te 2.
x=\frac{2\sqrt{7}+2}{4}
Nā, me whakaoti te whārite x=\frac{2±2\sqrt{7}}{4} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{7}.
x=\frac{\sqrt{7}+1}{2}
Whakawehe 2+2\sqrt{7} ki te 4.
x=\frac{2-2\sqrt{7}}{4}
Nā, me whakaoti te whārite x=\frac{2±2\sqrt{7}}{4} ina he tango te ±. Tango 2\sqrt{7} mai i 2.
x=\frac{1-\sqrt{7}}{2}
Whakawehe 2-2\sqrt{7} ki te 4.
x=\frac{\sqrt{7}+1}{2} x=\frac{1-\sqrt{7}}{2}
Kua oti te whārite te whakatau.
x-1=2x\left(-x+2\right)-x+2
Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+2.
x-1=-2x^{2}+4x-x+2
Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te -x+2.
x-1=-2x^{2}+3x+2
Pahekotia te 4x me -x, ka 3x.
x-1+2x^{2}=3x+2
Me tāpiri te 2x^{2} ki ngā taha e rua.
x-1+2x^{2}-3x=2
Tangohia te 3x mai i ngā taha e rua.
-2x-1+2x^{2}=2
Pahekotia te x me -3x, ka -2x.
-2x+2x^{2}=2+1
Me tāpiri te 1 ki ngā taha e rua.
-2x+2x^{2}=3
Tāpirihia te 2 ki te 1, ka 3.
2x^{2}-2x=3
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}-2x}{2}=\frac{3}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}+\left(-\frac{2}{2}\right)x=\frac{3}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}-x=\frac{3}{2}
Whakawehe -2 ki te 2.
x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{3}{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}=\frac{3}{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{7}{4}
Tāpiri \frac{3}{2} ki te \frac{1}{4} 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}{2}\right)^{2}=\frac{7}{4}
Tauwehea te x^{2}-x+\frac{1}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{7}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{1}{2}=\frac{\sqrt{7}}{2} x-\frac{1}{2}=-\frac{\sqrt{7}}{2}
Whakarūnātia.
x=\frac{\sqrt{7}+1}{2} x=\frac{1-\sqrt{7}}{2}
Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.