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x\left(14-7x\right)=0
Tauwehea te x.
x=0 x=2
Hei kimi otinga whārite, me whakaoti te x=0 me te 14-7x=0.
-7x^{2}+14x=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{-14±\sqrt{14^{2}}}{2\left(-7\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -7 mō a, 14 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-14±14}{2\left(-7\right)}
Tuhia te pūtakerua o te 14^{2}.
x=\frac{-14±14}{-14}
Whakareatia 2 ki te -7.
x=\frac{0}{-14}
Nā, me whakaoti te whārite x=\frac{-14±14}{-14} ina he tāpiri te ±. Tāpiri -14 ki te 14.
x=0
Whakawehe 0 ki te -14.
x=-\frac{28}{-14}
Nā, me whakaoti te whārite x=\frac{-14±14}{-14} ina he tango te ±. Tango 14 mai i -14.
x=2
Whakawehe -28 ki te -14.
x=0 x=2
Kua oti te whārite te whakatau.
-7x^{2}+14x=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{-7x^{2}+14x}{-7}=\frac{0}{-7}
Whakawehea ngā taha e rua ki te -7.
x^{2}+\frac{14}{-7}x=\frac{0}{-7}
Mā te whakawehe ki te -7 ka wetekia te whakareanga ki te -7.
x^{2}-2x=\frac{0}{-7}
Whakawehe 14 ki te -7.
x^{2}-2x=0
Whakawehe 0 ki te -7.
x^{2}-2x+1=1
Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
\left(x-1\right)^{2}=1
Tauwehea x^{2}-2x+1. 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-1\right)^{2}}=\sqrt{1}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-1=1 x-1=-1
Whakarūnātia.
x=2 x=0
Me tāpiri 1 ki ngā taha e rua o te whārite.