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

Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

x^{2}-\frac{5}{2}x-\frac{1}{2}=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(-\frac{5}{2}\right)±\sqrt{\left(-\frac{5}{2}\right)^{2}-4\left(-\frac{1}{2}\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -\frac{5}{2} mō b, me -\frac{1}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-\frac{5}{2}\right)±\sqrt{\frac{25}{4}-4\left(-\frac{1}{2}\right)}}{2}
Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x=\frac{-\left(-\frac{5}{2}\right)±\sqrt{\frac{25}{4}+2}}{2}
Whakareatia -4 ki te -\frac{1}{2}.
x=\frac{-\left(-\frac{5}{2}\right)±\sqrt{\frac{33}{4}}}{2}
Tāpiri \frac{25}{4} ki te 2.
x=\frac{-\left(-\frac{5}{2}\right)±\frac{\sqrt{33}}{2}}{2}
Tuhia te pūtakerua o te \frac{33}{4}.
x=\frac{\frac{5}{2}±\frac{\sqrt{33}}{2}}{2}
Ko te tauaro o -\frac{5}{2} ko \frac{5}{2}.
x=\frac{\sqrt{33}+5}{2\times 2}
Nā, me whakaoti te whārite x=\frac{\frac{5}{2}±\frac{\sqrt{33}}{2}}{2} ina he tāpiri te ±. Tāpiri \frac{5}{2} ki te \frac{\sqrt{33}}{2}.
x=\frac{\sqrt{33}+5}{4}
Whakawehe \frac{5+\sqrt{33}}{2} ki te 2.
x=\frac{5-\sqrt{33}}{2\times 2}
Nā, me whakaoti te whārite x=\frac{\frac{5}{2}±\frac{\sqrt{33}}{2}}{2} ina he tango te ±. Tango \frac{\sqrt{33}}{2} mai i \frac{5}{2}.
x=\frac{5-\sqrt{33}}{4}
Whakawehe \frac{5-\sqrt{33}}{2} ki te 2.
x=\frac{\sqrt{33}+5}{4} x=\frac{5-\sqrt{33}}{4}
Kua oti te whārite te whakatau.
x^{2}-\frac{5}{2}x-\frac{1}{2}=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.
x^{2}-\frac{5}{2}x-\frac{1}{2}-\left(-\frac{1}{2}\right)=-\left(-\frac{1}{2}\right)
Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.
x^{2}-\frac{5}{2}x=-\left(-\frac{1}{2}\right)
Mā te tango i te -\frac{1}{2} i a ia ake anō ka toe ko te 0.
x^{2}-\frac{5}{2}x=\frac{1}{2}
Tango -\frac{1}{2} mai i 0.
x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=\frac{1}{2}+\left(-\frac{5}{4}\right)^{2}
Whakawehea te -\frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{4}. Nā, tāpiria te pūrua o te -\frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{1}{2}+\frac{25}{16}
Pūruatia -\frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{33}{16}
Tāpiri \frac{1}{2} ki te \frac{25}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
\left(x-\frac{5}{4}\right)^{2}=\frac{33}{16}
Tauwehea x^{2}-\frac{5}{2}x+\frac{25}{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-\frac{5}{4}\right)^{2}}=\sqrt{\frac{33}{16}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-\frac{5}{4}=\frac{\sqrt{33}}{4} x-\frac{5}{4}=-\frac{\sqrt{33}}{4}
Whakarūnātia.
x=\frac{\sqrt{33}+5}{4} x=\frac{5-\sqrt{33}}{4}
Me tāpiri \frac{5}{4} ki ngā taha e rua o te whārite.