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8x-x^{2}=-9
Tangohia te x^{2} mai i ngā taha e rua.
8x-x^{2}+9=0
Me tāpiri te 9 ki ngā taha e rua.
-x^{2}+8x+9=0
Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.
a+b=8 ab=-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 tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -9.
-1+9=8 -3+3=0
Tātaihia te tapeke mō ia takirua.
a=9 b=-1
Ko te otinga te takirua ka hoatu i te tapeke 8.
\left(-x^{2}+9x\right)+\left(-x+9\right)
Tuhia anō te -x^{2}+8x+9 hei \left(-x^{2}+9x\right)+\left(-x+9\right).
-x\left(x-9\right)-\left(x-9\right)
Tauwehea te -x i te tuatahi me te -1 i te rōpū tuarua.
\left(x-9\right)\left(-x-1\right)
Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.
x=9 x=-1
Hei kimi otinga whārite, me whakaoti te x-9=0 me te -x-1=0.
8x-x^{2}=-9
Tangohia te x^{2} mai i ngā taha e rua.
8x-x^{2}+9=0
Me tāpiri te 9 ki ngā taha e rua.
-x^{2}+8x+9=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{-8±\sqrt{8^{2}-4\left(-1\right)\times 9}}{2\left(-1\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 8 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-8±\sqrt{64-4\left(-1\right)\times 9}}{2\left(-1\right)}
Pūrua 8.
x=\frac{-8±\sqrt{64+4\times 9}}{2\left(-1\right)}
Whakareatia -4 ki te -1.
x=\frac{-8±\sqrt{64+36}}{2\left(-1\right)}
Whakareatia 4 ki te 9.
x=\frac{-8±\sqrt{100}}{2\left(-1\right)}
Tāpiri 64 ki te 36.
x=\frac{-8±10}{2\left(-1\right)}
Tuhia te pūtakerua o te 100.
x=\frac{-8±10}{-2}
Whakareatia 2 ki te -1.
x=\frac{2}{-2}
Nā, me whakaoti te whārite x=\frac{-8±10}{-2} ina he tāpiri te ±. Tāpiri -8 ki te 10.
x=-1
Whakawehe 2 ki te -2.
x=-\frac{18}{-2}
Nā, me whakaoti te whārite x=\frac{-8±10}{-2} ina he tango te ±. Tango 10 mai i -8.
x=9
Whakawehe -18 ki te -2.
x=-1 x=9
Kua oti te whārite te whakatau.
8x-x^{2}=-9
Tangohia te x^{2} mai i ngā taha e rua.
-x^{2}+8x=-9
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.
\frac{-x^{2}+8x}{-1}=-\frac{9}{-1}
Whakawehea ngā taha e rua ki te -1.
x^{2}+\frac{8}{-1}x=-\frac{9}{-1}
Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.
x^{2}-8x=-\frac{9}{-1}
Whakawehe 8 ki te -1.
x^{2}-8x=9
Whakawehe -9 ki te -1.
x^{2}-8x+\left(-4\right)^{2}=9+\left(-4\right)^{2}
Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-8x+16=9+16
Pūrua -4.
x^{2}-8x+16=25
Tāpiri 9 ki te 16.
\left(x-4\right)^{2}=25
Tauwehea x^{2}-8x+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-4\right)^{2}}=\sqrt{25}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-4=5 x-4=-5
Whakarūnātia.
x=9 x=-1
Me tāpiri 4 ki ngā taha e rua o te whārite.