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4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)
Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.
4x^{2}+8+x+7=12+3\left(x^{2}+1\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.
4x^{2}+15+x=12+3\left(x^{2}+1\right)
Tāpirihia te 8 ki te 7, ka 15.
4x^{2}+15+x=12+3x^{2}+3
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.
4x^{2}+15+x=15+3x^{2}
Tāpirihia te 12 ki te 3, ka 15.
4x^{2}+15+x-15=3x^{2}
Tangohia te 15 mai i ngā taha e rua.
4x^{2}+x=3x^{2}
Tangohia te 15 i te 15, ka 0.
4x^{2}+x-3x^{2}=0
Tangohia te 3x^{2} mai i ngā taha e rua.
x^{2}+x=0
Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.
x\left(x+1\right)=0
Tauwehea te x.
x=0 x=-1
Hei kimi otinga whārite, me whakaoti te x=0 me te x+1=0.
4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)
Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.
4x^{2}+8+x+7=12+3\left(x^{2}+1\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.
4x^{2}+15+x=12+3\left(x^{2}+1\right)
Tāpirihia te 8 ki te 7, ka 15.
4x^{2}+15+x=12+3x^{2}+3
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.
4x^{2}+15+x=15+3x^{2}
Tāpirihia te 12 ki te 3, ka 15.
4x^{2}+15+x-15=3x^{2}
Tangohia te 15 mai i ngā taha e rua.
4x^{2}+x=3x^{2}
Tangohia te 15 i te 15, ka 0.
4x^{2}+x-3x^{2}=0
Tangohia te 3x^{2} mai i ngā taha e rua.
x^{2}+x=0
Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.
x=\frac{-1±\sqrt{1^{2}}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1±1}{2}
Tuhia te pūtakerua o te 1^{2}.
x=\frac{0}{2}
Nā, me whakaoti te whārite x=\frac{-1±1}{2} ina he tāpiri te ±. Tāpiri -1 ki te 1.
x=0
Whakawehe 0 ki te 2.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{-1±1}{2} ina he tango te ±. Tango 1 mai i -1.
x=-1
Whakawehe -2 ki te 2.
x=0 x=-1
Kua oti te whārite te whakatau.
4\left(x^{2}+2\right)+x+7=12+3\left(x^{2}+1\right)
Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,12,4.
4x^{2}+8+x+7=12+3\left(x^{2}+1\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2.
4x^{2}+15+x=12+3\left(x^{2}+1\right)
Tāpirihia te 8 ki te 7, ka 15.
4x^{2}+15+x=12+3x^{2}+3
Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}+1.
4x^{2}+15+x=15+3x^{2}
Tāpirihia te 12 ki te 3, ka 15.
4x^{2}+15+x-15=3x^{2}
Tangohia te 15 mai i ngā taha e rua.
4x^{2}+x=3x^{2}
Tangohia te 15 i te 15, ka 0.
4x^{2}+x-3x^{2}=0
Tangohia te 3x^{2} mai i ngā taha e rua.
x^{2}+x=0
Pahekotia te 4x^{2} me -3x^{2}, ka x^{2}.
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=0 x=-1
Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.