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x\left(3x-24\right)=0
Tauwehea te x.
x=0 x=8
Hei kimi otinga whārite, me whakaoti te x=0 me te 3x-24=0.
3x^{2}-24x=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(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 3}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -24 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-24\right)±24}{2\times 3}
Tuhia te pūtakerua o te \left(-24\right)^{2}.
x=\frac{24±24}{2\times 3}
Ko te tauaro o -24 ko 24.
x=\frac{24±24}{6}
Whakareatia 2 ki te 3.
x=\frac{48}{6}
Nā, me whakaoti te whārite x=\frac{24±24}{6} ina he tāpiri te ±. Tāpiri 24 ki te 24.
x=8
Whakawehe 48 ki te 6.
x=\frac{0}{6}
Nā, me whakaoti te whārite x=\frac{24±24}{6} ina he tango te ±. Tango 24 mai i 24.
x=0
Whakawehe 0 ki te 6.
x=8 x=0
Kua oti te whārite te whakatau.
3x^{2}-24x=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{3x^{2}-24x}{3}=\frac{0}{3}
Whakawehea ngā taha e rua ki te 3.
x^{2}+\left(-\frac{24}{3}\right)x=\frac{0}{3}
Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.
x^{2}-8x=\frac{0}{3}
Whakawehe -24 ki te 3.
x^{2}-8x=0
Whakawehe 0 ki te 3.
x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}
Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-8x+16=16
Pūrua -4.
\left(x-4\right)^{2}=16
Tauwehea x^{2}-8x+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-4\right)^{2}}=\sqrt{16}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-4=4 x-4=-4
Whakarūnātia.
x=8 x=0
Me tāpiri 4 ki ngā taha e rua o te whārite.