Tīpoka ki ngā ihirangi matua
Whakaoti mō x
Tick mark Image
Graph

Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

x^{2}+x-2=4
Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+2 ka whakakotahi i ngā kupu rite.
x^{2}+x-2-4=0
Tangohia te 4 mai i ngā taha e rua.
x^{2}+x-6=0
Tangohia te 4 i te -2, ka -6.
x=\frac{-1±\sqrt{1^{2}-4\left(-6\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-1±\sqrt{1-4\left(-6\right)}}{2}
Pūrua 1.
x=\frac{-1±\sqrt{1+24}}{2}
Whakareatia -4 ki te -6.
x=\frac{-1±\sqrt{25}}{2}
Tāpiri 1 ki te 24.
x=\frac{-1±5}{2}
Tuhia te pūtakerua o te 25.
x=\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{-1±5}{2} ina he tāpiri te ±. Tāpiri -1 ki te 5.
x=2
Whakawehe 4 ki te 2.
x=-\frac{6}{2}
Nā, me whakaoti te whārite x=\frac{-1±5}{2} ina he tango te ±. Tango 5 mai i -1.
x=-3
Whakawehe -6 ki te 2.
x=2 x=-3
Kua oti te whārite te whakatau.
x^{2}+x-2=4
Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x+2 ka whakakotahi i ngā kupu rite.
x^{2}+x=4+2
Me tāpiri te 2 ki ngā taha e rua.
x^{2}+x=6
Tāpirihia te 4 ki te 2, ka 6.
x^{2}+x+\left(\frac{1}{2}\right)^{2}=6+\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}=6+\frac{1}{4}
Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+x+\frac{1}{4}=\frac{25}{4}
Tāpiri 6 ki te \frac{1}{4}.
\left(x+\frac{1}{2}\right)^{2}=\frac{25}{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{25}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{1}{2}=\frac{5}{2} x+\frac{1}{2}=-\frac{5}{2}
Whakarūnātia.
x=2 x=-3
Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.