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2\left(-x^{2}+x+30\right)
Tauwehea te 2.
a+b=1 ab=-30=-30
Whakaarohia te -x^{2}+x+30. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,30 -2,15 -3,10 -5,6
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 -30.
-1+30=29 -2+15=13 -3+10=7 -5+6=1
Tātaihia te tapeke mō ia takirua.
a=6 b=-5
Ko te otinga te takirua ka hoatu i te tapeke 1.
\left(-x^{2}+6x\right)+\left(-5x+30\right)
Tuhia anō te -x^{2}+x+30 hei \left(-x^{2}+6x\right)+\left(-5x+30\right).
-x\left(x-6\right)-5\left(x-6\right)
Tauwehea te -x i te tuatahi me te -5 i te rōpū tuarua.
\left(x-6\right)\left(-x-5\right)
Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.
2\left(x-6\right)\left(-x-5\right)
Me tuhi anō te kīanga whakatauwehe katoa.
-2x^{2}+2x+60=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{-2±\sqrt{2^{2}-4\left(-2\right)\times 60}}{2\left(-2\right)}
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{-2±\sqrt{4-4\left(-2\right)\times 60}}{2\left(-2\right)}
Pūrua 2.
x=\frac{-2±\sqrt{4+8\times 60}}{2\left(-2\right)}
Whakareatia -4 ki te -2.
x=\frac{-2±\sqrt{4+480}}{2\left(-2\right)}
Whakareatia 8 ki te 60.
x=\frac{-2±\sqrt{484}}{2\left(-2\right)}
Tāpiri 4 ki te 480.
x=\frac{-2±22}{2\left(-2\right)}
Tuhia te pūtakerua o te 484.
x=\frac{-2±22}{-4}
Whakareatia 2 ki te -2.
x=\frac{20}{-4}
Nā, me whakaoti te whārite x=\frac{-2±22}{-4} ina he tāpiri te ±. Tāpiri -2 ki te 22.
x=-5
Whakawehe 20 ki te -4.
x=-\frac{24}{-4}
Nā, me whakaoti te whārite x=\frac{-2±22}{-4} ina he tango te ±. Tango 22 mai i -2.
x=6
Whakawehe -24 ki te -4.
-2x^{2}+2x+60=-2\left(x-\left(-5\right)\right)\left(x-6\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 6 mō te x_{2}.
-2x^{2}+2x+60=-2\left(x+5\right)\left(x-6\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.