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a+b=-6 ab=1\left(-27\right)=-27
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-27. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-27 3,-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 -27.
1-27=-26 3-9=-6
Tātaihia te tapeke mō ia takirua.
a=-9 b=3
Ko te otinga te takirua ka hoatu i te tapeke -6.
\left(x^{2}-9x\right)+\left(3x-27\right)
Tuhia anō te x^{2}-6x-27 hei \left(x^{2}-9x\right)+\left(3x-27\right).
x\left(x-9\right)+3\left(x-9\right)
Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.
\left(x-9\right)\left(x+3\right)
Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-6x-27=0
Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.
x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-27\right)}}{2}
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(-6\right)±\sqrt{36-4\left(-27\right)}}{2}
Pūrua -6.
x=\frac{-\left(-6\right)±\sqrt{36+108}}{2}
Whakareatia -4 ki te -27.
x=\frac{-\left(-6\right)±\sqrt{144}}{2}
Tāpiri 36 ki te 108.
x=\frac{-\left(-6\right)±12}{2}
Tuhia te pūtakerua o te 144.
x=\frac{6±12}{2}
Ko te tauaro o -6 ko 6.
x=\frac{18}{2}
Nā, me whakaoti te whārite x=\frac{6±12}{2} ina he tāpiri te ±. Tāpiri 6 ki te 12.
x=9
Whakawehe 18 ki te 2.
x=-\frac{6}{2}
Nā, me whakaoti te whārite x=\frac{6±12}{2} ina he tango te ±. Tango 12 mai i 6.
x=-3
Whakawehe -6 ki te 2.
x^{2}-6x-27=\left(x-9\right)\left(x-\left(-3\right)\right)
Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 9 mō te x_{1} me te -3 mō te x_{2}.
x^{2}-6x-27=\left(x-9\right)\left(x+3\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.