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3x^{2}-2x=12
Tangohia te 2x mai i ngā taha e rua.
3x^{2}-2x-12=0
Tangohia te 12 mai i ngā taha e rua.
x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3\left(-12\right)}}{2\times 3}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -2 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\times 3\left(-12\right)}}{2\times 3}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4-12\left(-12\right)}}{2\times 3}
Whakareatia -4 ki te 3.
x=\frac{-\left(-2\right)±\sqrt{4+144}}{2\times 3}
Whakareatia -12 ki te -12.
x=\frac{-\left(-2\right)±\sqrt{148}}{2\times 3}
Tāpiri 4 ki te 144.
x=\frac{-\left(-2\right)±2\sqrt{37}}{2\times 3}
Tuhia te pūtakerua o te 148.
x=\frac{2±2\sqrt{37}}{2\times 3}
Ko te tauaro o -2 ko 2.
x=\frac{2±2\sqrt{37}}{6}
Whakareatia 2 ki te 3.
x=\frac{2\sqrt{37}+2}{6}
Nā, me whakaoti te whārite x=\frac{2±2\sqrt{37}}{6} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{37}.
x=\frac{\sqrt{37}+1}{3}
Whakawehe 2+2\sqrt{37} ki te 6.
x=\frac{2-2\sqrt{37}}{6}
Nā, me whakaoti te whārite x=\frac{2±2\sqrt{37}}{6} ina he tango te ±. Tango 2\sqrt{37} mai i 2.
x=\frac{1-\sqrt{37}}{3}
Whakawehe 2-2\sqrt{37} ki te 6.
x=\frac{\sqrt{37}+1}{3} x=\frac{1-\sqrt{37}}{3}
Kua oti te whārite te whakatau.
3x^{2}-2x=12
Tangohia te 2x mai i ngā taha e rua.
\frac{3x^{2}-2x}{3}=\frac{12}{3}
Whakawehea ngā taha e rua ki te 3.
x^{2}-\frac{2}{3}x=\frac{12}{3}
Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.
x^{2}-\frac{2}{3}x=4
Whakawehe 12 ki te 3.
x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=4+\left(-\frac{1}{3}\right)^{2}
Whakawehea te -\frac{2}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{3}. Nā, tāpiria te pūrua o te -\frac{1}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{2}{3}x+\frac{1}{9}=4+\frac{1}{9}
Pūruatia -\frac{1}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{37}{9}
Tāpiri 4 ki te \frac{1}{9}.
\left(x-\frac{1}{3}\right)^{2}=\frac{37}{9}
Tauwehea x^{2}-\frac{2}{3}x+\frac{1}{9}. 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}{3}\right)^{2}}=\sqrt{\frac{37}{9}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{1}{3}=\frac{\sqrt{37}}{3} x-\frac{1}{3}=-\frac{\sqrt{37}}{3}
Whakarūnātia.
x=\frac{\sqrt{37}+1}{3} x=\frac{1-\sqrt{37}}{3}
Me tāpiri \frac{1}{3} ki ngā taha e rua o te whārite.