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0.5x^{2}-2x=-2
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.
0.5x^{2}-2x-\left(-2\right)=-2-\left(-2\right)
Me tāpiri 2 ki ngā taha e rua o te whārite.
0.5x^{2}-2x-\left(-2\right)=0
Mā te tango i te -2 i a ia ake anō ka toe ko te 0.
0.5x^{2}-2x+2=0
Tango -2 mai i 0.
x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 0.5\times 2}}{2\times 0.5}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.5 mō a, -2 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-2\right)±\sqrt{4-4\times 0.5\times 2}}{2\times 0.5}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4-2\times 2}}{2\times 0.5}
Whakareatia -4 ki te 0.5.
x=\frac{-\left(-2\right)±\sqrt{4-4}}{2\times 0.5}
Whakareatia -2 ki te 2.
x=\frac{-\left(-2\right)±\sqrt{0}}{2\times 0.5}
Tāpiri 4 ki te -4.
x=-\frac{-2}{2\times 0.5}
Tuhia te pūtakerua o te 0.
x=\frac{2}{2\times 0.5}
Ko te tauaro o -2 ko 2.
x=\frac{2}{1}
Whakareatia 2 ki te 0.5.
0.5x^{2}-2x=-2
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{0.5x^{2}-2x}{0.5}=-\frac{2}{0.5}
Me whakarea ngā taha e rua ki te 2.
x^{2}+\left(-\frac{2}{0.5}\right)x=-\frac{2}{0.5}
Mā te whakawehe ki te 0.5 ka wetekia te whakareanga ki te 0.5.
x^{2}-4x=-\frac{2}{0.5}
Whakawehe -2 ki te 0.5 mā te whakarea -2 ki te tau huripoki o 0.5.
x^{2}-4x=-4
Whakawehe -2 ki te 0.5 mā te whakarea -2 ki te tau huripoki o 0.5.
x^{2}-4x+\left(-2\right)^{2}=-4+\left(-2\right)^{2}
Whakawehea te -4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -2. Nā, tāpiria te pūrua o te -2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-4x+4=-4+4
Pūrua -2.
x^{2}-4x+4=0
Tāpiri -4 ki te 4.
\left(x-2\right)^{2}=0
Tauwehea x^{2}-4x+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-2\right)^{2}}=\sqrt{0}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-2=0 x-2=0
Whakarūnātia.
x=2 x=2
Me tāpiri 2 ki ngā taha e rua o te whārite.
x=2
Kua oti te whārite te whakatau. He ōrite ngā whakatau.