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x\left(\frac{5}{3}x+2\right)=0
Tauwehea te x.
x=0 x=-\frac{6}{5}
Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{5x}{3}+2=0.
\frac{5}{3}x^{2}+2x=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{-2±\sqrt{2^{2}}}{2\times \frac{5}{3}}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{5}{3} mō a, 2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±2}{2\times \frac{5}{3}}
Tuhia te pūtakerua o te 2^{2}.
x=\frac{-2±2}{\frac{10}{3}}
Whakareatia 2 ki te \frac{5}{3}.
x=\frac{0}{\frac{10}{3}}
Nā, me whakaoti te whārite x=\frac{-2±2}{\frac{10}{3}} ina he tāpiri te ±. Tāpiri -2 ki te 2.
x=0
Whakawehe 0 ki te \frac{10}{3} mā te whakarea 0 ki te tau huripoki o \frac{10}{3}.
x=-\frac{4}{\frac{10}{3}}
Nā, me whakaoti te whārite x=\frac{-2±2}{\frac{10}{3}} ina he tango te ±. Tango 2 mai i -2.
x=-\frac{6}{5}
Whakawehe -4 ki te \frac{10}{3} mā te whakarea -4 ki te tau huripoki o \frac{10}{3}.
x=0 x=-\frac{6}{5}
Kua oti te whārite te whakatau.
\frac{5}{3}x^{2}+2x=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{\frac{5}{3}x^{2}+2x}{\frac{5}{3}}=\frac{0}{\frac{5}{3}}
Whakawehea ngā taha e rua o te whārite ki te \frac{5}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.
x^{2}+\frac{2}{\frac{5}{3}}x=\frac{0}{\frac{5}{3}}
Mā te whakawehe ki te \frac{5}{3} ka wetekia te whakareanga ki te \frac{5}{3}.
x^{2}+\frac{6}{5}x=\frac{0}{\frac{5}{3}}
Whakawehe 2 ki te \frac{5}{3} mā te whakarea 2 ki te tau huripoki o \frac{5}{3}.
x^{2}+\frac{6}{5}x=0
Whakawehe 0 ki te \frac{5}{3} mā te whakarea 0 ki te tau huripoki o \frac{5}{3}.
x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\left(\frac{3}{5}\right)^{2}
Whakawehea te \frac{6}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{5}. Nā, tāpiria te pūrua o te \frac{3}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}
Pūruatia \frac{3}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.
\left(x+\frac{3}{5}\right)^{2}=\frac{9}{25}
Tauwehea x^{2}+\frac{6}{5}x+\frac{9}{25}. 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{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{3}{5}=\frac{3}{5} x+\frac{3}{5}=-\frac{3}{5}
Whakarūnātia.
x=0 x=-\frac{6}{5}
Me tango \frac{3}{5} mai i ngā taha e rua o te whārite.