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2x^{2}-2x=x-1
Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.
2x^{2}-2x-x=-1
Tangohia te x mai i ngā taha e rua.
2x^{2}-3x=-1
Pahekotia te -2x me -x, ka -3x.
2x^{2}-3x+1=0
Me tāpiri te 1 ki ngā taha e rua.
x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2}}{2\times 2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -3 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-3\right)±\sqrt{9-4\times 2}}{2\times 2}
Pūrua -3.
x=\frac{-\left(-3\right)±\sqrt{9-8}}{2\times 2}
Whakareatia -4 ki te 2.
x=\frac{-\left(-3\right)±\sqrt{1}}{2\times 2}
Tāpiri 9 ki te -8.
x=\frac{-\left(-3\right)±1}{2\times 2}
Tuhia te pūtakerua o te 1.
x=\frac{3±1}{2\times 2}
Ko te tauaro o -3 ko 3.
x=\frac{3±1}{4}
Whakareatia 2 ki te 2.
x=\frac{4}{4}
Nā, me whakaoti te whārite x=\frac{3±1}{4} ina he tāpiri te ±. Tāpiri 3 ki te 1.
x=1
Whakawehe 4 ki te 4.
x=\frac{2}{4}
Nā, me whakaoti te whārite x=\frac{3±1}{4} ina he tango te ±. Tango 1 mai i 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=1 x=\frac{1}{2}
Kua oti te whārite te whakatau.
2x^{2}-2x=x-1
Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.
2x^{2}-2x-x=-1
Tangohia te x mai i ngā taha e rua.
2x^{2}-3x=-1
Pahekotia te -2x me -x, ka -3x.
\frac{2x^{2}-3x}{2}=-\frac{1}{2}
Whakawehea ngā taha e rua ki te 2.
x^{2}-\frac{3}{2}x=-\frac{1}{2}
Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.
x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=-\frac{1}{2}+\left(-\frac{3}{4}\right)^{2}
Whakawehea te -\frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{4}. Nā, tāpiria te pūrua o te -\frac{3}{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{3}{2}x+\frac{9}{16}=-\frac{1}{2}+\frac{9}{16}
Pūruatia -\frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{1}{16}
Tāpiri -\frac{1}{2} ki te \frac{9}{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{3}{4}\right)^{2}=\frac{1}{16}
Tauwehea x^{2}-\frac{3}{2}x+\frac{9}{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{3}{4}\right)^{2}}=\sqrt{\frac{1}{16}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{3}{4}=\frac{1}{4} x-\frac{3}{4}=-\frac{1}{4}
Whakarūnātia.
x=1 x=\frac{1}{2}
Me tāpiri \frac{3}{4} ki ngā taha e rua o te whārite.