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z^{2}+27-10z=0
Tangohia te 10z mai i ngā taha e rua.
z^{2}-10z+27=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.
z=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 27}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me 27 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
z=\frac{-\left(-10\right)±\sqrt{100-4\times 27}}{2}
Pūrua -10.
z=\frac{-\left(-10\right)±\sqrt{100-108}}{2}
Whakareatia -4 ki te 27.
z=\frac{-\left(-10\right)±\sqrt{-8}}{2}
Tāpiri 100 ki te -108.
z=\frac{-\left(-10\right)±2\sqrt{2}i}{2}
Tuhia te pūtakerua o te -8.
z=\frac{10±2\sqrt{2}i}{2}
Ko te tauaro o -10 ko 10.
z=\frac{10+2\sqrt{2}i}{2}
Nā, me whakaoti te whārite z=\frac{10±2\sqrt{2}i}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2i\sqrt{2}.
z=5+\sqrt{2}i
Whakawehe 10+2i\sqrt{2} ki te 2.
z=\frac{-2\sqrt{2}i+10}{2}
Nā, me whakaoti te whārite z=\frac{10±2\sqrt{2}i}{2} ina he tango te ±. Tango 2i\sqrt{2} mai i 10.
z=-\sqrt{2}i+5
Whakawehe 10-2i\sqrt{2} ki te 2.
z=5+\sqrt{2}i z=-\sqrt{2}i+5
Kua oti te whārite te whakatau.
z^{2}+27-10z=0
Tangohia te 10z mai i ngā taha e rua.
z^{2}-10z=-27
Tangohia te 27 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
z^{2}-10z+\left(-5\right)^{2}=-27+\left(-5\right)^{2}
Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
z^{2}-10z+25=-27+25
Pūrua -5.
z^{2}-10z+25=-2
Tāpiri -27 ki te 25.
\left(z-5\right)^{2}=-2
Tauwehea z^{2}-10z+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(z-5\right)^{2}}=\sqrt{-2}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
z-5=\sqrt{2}i z-5=-\sqrt{2}i
Whakarūnātia.
z=5+\sqrt{2}i z=-\sqrt{2}i+5
Me tāpiri 5 ki ngā taha e rua o te whārite.