Whakaoti mō x
x=1
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Tohaina
Kua tāruatia ki te papatopenga
2x\times 3=2\times 1x+x\times 4x
Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x,x^{2},2x.
2x\times 3=2\times 1x+x^{2}\times 4
Whakareatia te x ki te x, ka x^{2}.
6x=2\times 1x+x^{2}\times 4
Whakareatia te 2 ki te 3, ka 6.
6x=2x+x^{2}\times 4
Whakareatia te 2 ki te 1, ka 2.
6x-2x=x^{2}\times 4
Tangohia te 2x mai i ngā taha e rua.
4x=x^{2}\times 4
Pahekotia te 6x me -2x, ka 4x.
4x-x^{2}\times 4=0
Tangohia te x^{2}\times 4 mai i ngā taha e rua.
4x-4x^{2}=0
Whakareatia te -1 ki te 4, ka -4.
x\left(4-4x\right)=0
Tauwehea te x.
x=0 x=1
Hei kimi otinga whārite, me whakaoti te x=0 me te 4-4x=0.
x=1
Tē taea kia ōrite te tāupe x ki 0.
2x\times 3=2\times 1x+x\times 4x
Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x,x^{2},2x.
2x\times 3=2\times 1x+x^{2}\times 4
Whakareatia te x ki te x, ka x^{2}.
6x=2\times 1x+x^{2}\times 4
Whakareatia te 2 ki te 3, ka 6.
6x=2x+x^{2}\times 4
Whakareatia te 2 ki te 1, ka 2.
6x-2x=x^{2}\times 4
Tangohia te 2x mai i ngā taha e rua.
4x=x^{2}\times 4
Pahekotia te 6x me -2x, ka 4x.
4x-x^{2}\times 4=0
Tangohia te x^{2}\times 4 mai i ngā taha e rua.
4x-4x^{2}=0
Whakareatia te -1 ki te 4, ka -4.
-4x^{2}+4x=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{-4±\sqrt{4^{2}}}{2\left(-4\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 4 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±4}{2\left(-4\right)}
Tuhia te pūtakerua o te 4^{2}.
x=\frac{-4±4}{-8}
Whakareatia 2 ki te -4.
x=\frac{0}{-8}
Nā, me whakaoti te whārite x=\frac{-4±4}{-8} ina he tāpiri te ±. Tāpiri -4 ki te 4.
x=0
Whakawehe 0 ki te -8.
x=-\frac{8}{-8}
Nā, me whakaoti te whārite x=\frac{-4±4}{-8} ina he tango te ±. Tango 4 mai i -4.
x=1
Whakawehe -8 ki te -8.
x=0 x=1
Kua oti te whārite te whakatau.
x=1
Tē taea kia ōrite te tāupe x ki 0.
2x\times 3=2\times 1x+x\times 4x
Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o x,x^{2},2x.
2x\times 3=2\times 1x+x^{2}\times 4
Whakareatia te x ki te x, ka x^{2}.
6x=2\times 1x+x^{2}\times 4
Whakareatia te 2 ki te 3, ka 6.
6x=2x+x^{2}\times 4
Whakareatia te 2 ki te 1, ka 2.
6x-2x=x^{2}\times 4
Tangohia te 2x mai i ngā taha e rua.
4x=x^{2}\times 4
Pahekotia te 6x me -2x, ka 4x.
4x-x^{2}\times 4=0
Tangohia te x^{2}\times 4 mai i ngā taha e rua.
4x-4x^{2}=0
Whakareatia te -1 ki te 4, ka -4.
-4x^{2}+4x=0
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{-4x^{2}+4x}{-4}=\frac{0}{-4}
Whakawehea ngā taha e rua ki te -4.
x^{2}+\frac{4}{-4}x=\frac{0}{-4}
Mā te whakawehe ki te -4 ka wetekia te whakareanga ki te -4.
x^{2}-x=\frac{0}{-4}
Whakawehe 4 ki te -4.
x^{2}-x=0
Whakawehe 0 ki te -4.
x^{2}-x+\left(-\frac{1}{2}\right)^{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{1}{4}
Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
\left(x-\frac{1}{2}\right)^{2}=\frac{1}{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{1}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{1}{2}=\frac{1}{2} x-\frac{1}{2}=-\frac{1}{2}
Whakarūnātia.
x=1 x=0
Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.
x=1
Tē taea kia ōrite te tāupe x ki 0.
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