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3x^{2}-18x+32-5=0
Tangohia te 5 mai i ngā taha e rua.
3x^{2}-18x+27=0
Tangohia te 5 i te 32, ka 27.
x^{2}-6x+9=0
Whakawehea ngā taha e rua ki te 3.
a+b=-6 ab=1\times 9=9
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-9 -3,-3
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 9.
-1-9=-10 -3-3=-6
Tātaihia te tapeke mō ia takirua.
a=-3 b=-3
Ko te otinga te takirua ka hoatu i te tapeke -6.
\left(x^{2}-3x\right)+\left(-3x+9\right)
Tuhia anō te x^{2}-6x+9 hei \left(x^{2}-3x\right)+\left(-3x+9\right).
x\left(x-3\right)-3\left(x-3\right)
Tauwehea te x i te tuatahi me te -3 i te rōpū tuarua.
\left(x-3\right)\left(x-3\right)
Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x-3\right)^{2}
Tuhia anōtia hei pūrua huarua.
x=3
Hei kimi i te otinga whārite, whakaotia te x-3=0.
3x^{2}-18x+32=5
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.
3x^{2}-18x+32-5=5-5
Me tango 5 mai i ngā taha e rua o te whārite.
3x^{2}-18x+32-5=0
Mā te tango i te 5 i a ia ake anō ka toe ko te 0.
3x^{2}-18x+27=0
Tango 5 mai i 32.
x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 3\times 27}}{2\times 3}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -18 mō b, me 27 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-18\right)±\sqrt{324-4\times 3\times 27}}{2\times 3}
Pūrua -18.
x=\frac{-\left(-18\right)±\sqrt{324-12\times 27}}{2\times 3}
Whakareatia -4 ki te 3.
x=\frac{-\left(-18\right)±\sqrt{324-324}}{2\times 3}
Whakareatia -12 ki te 27.
x=\frac{-\left(-18\right)±\sqrt{0}}{2\times 3}
Tāpiri 324 ki te -324.
x=-\frac{-18}{2\times 3}
Tuhia te pūtakerua o te 0.
x=\frac{18}{2\times 3}
Ko te tauaro o -18 ko 18.
x=\frac{18}{6}
Whakareatia 2 ki te 3.
x=3
Whakawehe 18 ki te 6.
3x^{2}-18x+32=5
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.
3x^{2}-18x+32-32=5-32
Me tango 32 mai i ngā taha e rua o te whārite.
3x^{2}-18x=5-32
Mā te tango i te 32 i a ia ake anō ka toe ko te 0.
3x^{2}-18x=-27
Tango 32 mai i 5.
\frac{3x^{2}-18x}{3}=-\frac{27}{3}
Whakawehea ngā taha e rua ki te 3.
x^{2}+\left(-\frac{18}{3}\right)x=-\frac{27}{3}
Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.
x^{2}-6x=-\frac{27}{3}
Whakawehe -18 ki te 3.
x^{2}-6x=-9
Whakawehe -27 ki te 3.
x^{2}-6x+\left(-3\right)^{2}=-9+\left(-3\right)^{2}
Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-6x+9=-9+9
Pūrua -3.
x^{2}-6x+9=0
Tāpiri -9 ki te 9.
\left(x-3\right)^{2}=0
Tauwehea x^{2}-6x+9. 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-3\right)^{2}}=\sqrt{0}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-3=0 x-3=0
Whakarūnātia.
x=3 x=3
Me tāpiri 3 ki ngā taha e rua o te whārite.
x=3
Kua oti te whārite te whakatau. He ōrite ngā whakatau.