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a+b=-1 ab=1\left(-20\right)=-20
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-20 2,-10 4,-5
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 -20.
1-20=-19 2-10=-8 4-5=-1
Tātaihia te tapeke mō ia takirua.
a=-5 b=4
Ko te otinga te takirua ka hoatu i te tapeke -1.
\left(x^{2}-5x\right)+\left(4x-20\right)
Tuhia anō te x^{2}-x-20 hei \left(x^{2}-5x\right)+\left(4x-20\right).
x\left(x-5\right)+4\left(x-5\right)
Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.
\left(x-5\right)\left(x+4\right)
Whakatauwehea atu te kīanga pātahi x-5 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-x-20=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(-1\right)±\sqrt{1-4\left(-20\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(-1\right)±\sqrt{1+80}}{2}
Whakareatia -4 ki te -20.
x=\frac{-\left(-1\right)±\sqrt{81}}{2}
Tāpiri 1 ki te 80.
x=\frac{-\left(-1\right)±9}{2}
Tuhia te pūtakerua o te 81.
x=\frac{1±9}{2}
Ko te tauaro o -1 ko 1.
x=\frac{10}{2}
Nā, me whakaoti te whārite x=\frac{1±9}{2} ina he tāpiri te ±. Tāpiri 1 ki te 9.
x=5
Whakawehe 10 ki te 2.
x=-\frac{8}{2}
Nā, me whakaoti te whārite x=\frac{1±9}{2} ina he tango te ±. Tango 9 mai i 1.
x=-4
Whakawehe -8 ki te 2.
x^{2}-x-20=\left(x-5\right)\left(x-\left(-4\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 5 mō te x_{1} me te -4 mō te x_{2}.
x^{2}-x-20=\left(x-5\right)\left(x+4\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.