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x^{2}-18x-63=0
Tangohia te 63 mai i ngā taha e rua.
a+b=-18 ab=-63
Hei whakaoti i te whārite, whakatauwehea te x^{2}-18x-63 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-63 3,-21 7,-9
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -63.
1-63=-62 3-21=-18 7-9=-2
Tātaihia te tapeke mō ia takirua.
a=-21 b=3
Ko te otinga te takirua ka hoatu i te tapeke -18.
\left(x-21\right)\left(x+3\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=21 x=-3
Hei kimi otinga whārite, me whakaoti te x-21=0 me te x+3=0.
x^{2}-18x-63=0
Tangohia te 63 mai i ngā taha e rua.
a+b=-18 ab=1\left(-63\right)=-63
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-63. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-63 3,-21 7,-9
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -63.
1-63=-62 3-21=-18 7-9=-2
Tātaihia te tapeke mō ia takirua.
a=-21 b=3
Ko te otinga te takirua ka hoatu i te tapeke -18.
\left(x^{2}-21x\right)+\left(3x-63\right)
Tuhia anō te x^{2}-18x-63 hei \left(x^{2}-21x\right)+\left(3x-63\right).
x\left(x-21\right)+3\left(x-21\right)
Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.
\left(x-21\right)\left(x+3\right)
Whakatauwehea atu te kīanga pātahi x-21 mā te whakamahi i te āhuatanga tātai tohatoha.
x=21 x=-3
Hei kimi otinga whārite, me whakaoti te x-21=0 me te x+3=0.
x^{2}-18x=63
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^{2}-18x-63=63-63
Me tango 63 mai i ngā taha e rua o te whārite.
x^{2}-18x-63=0
Mā te tango i te 63 i a ia ake anō ka toe ko te 0.
x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\left(-63\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -18 mō b, me -63 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-18\right)±\sqrt{324-4\left(-63\right)}}{2}
Pūrua -18.
x=\frac{-\left(-18\right)±\sqrt{324+252}}{2}
Whakareatia -4 ki te -63.
x=\frac{-\left(-18\right)±\sqrt{576}}{2}
Tāpiri 324 ki te 252.
x=\frac{-\left(-18\right)±24}{2}
Tuhia te pūtakerua o te 576.
x=\frac{18±24}{2}
Ko te tauaro o -18 ko 18.
x=\frac{42}{2}
Nā, me whakaoti te whārite x=\frac{18±24}{2} ina he tāpiri te ±. Tāpiri 18 ki te 24.
x=21
Whakawehe 42 ki te 2.
x=-\frac{6}{2}
Nā, me whakaoti te whārite x=\frac{18±24}{2} ina he tango te ±. Tango 24 mai i 18.
x=-3
Whakawehe -6 ki te 2.
x=21 x=-3
Kua oti te whārite te whakatau.
x^{2}-18x=63
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}-18x+\left(-9\right)^{2}=63+\left(-9\right)^{2}
Whakawehea te -18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -9. Nā, tāpiria te pūrua o te -9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-18x+81=63+81
Pūrua -9.
x^{2}-18x+81=144
Tāpiri 63 ki te 81.
\left(x-9\right)^{2}=144
Tauwehea x^{2}-18x+81. 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-9\right)^{2}}=\sqrt{144}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-9=12 x-9=-12
Whakarūnātia.
x=21 x=-3
Me tāpiri 9 ki ngā taha e rua o te whārite.