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a+b=-17 ab=-2\times 30=-60
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -2x^{2}+ax+bx+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-60 2,-30 3,-20 4,-15 5,-12 6,-10
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 -60.
1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4
Tātaihia te tapeke mō ia takirua.
a=3 b=-20
Ko te otinga te takirua ka hoatu i te tapeke -17.
\left(-2x^{2}+3x\right)+\left(-20x+30\right)
Tuhia anō te -2x^{2}-17x+30 hei \left(-2x^{2}+3x\right)+\left(-20x+30\right).
-x\left(2x-3\right)-10\left(2x-3\right)
Tauwehea te -x i te tuatahi me te -10 i te rōpū tuarua.
\left(2x-3\right)\left(-x-10\right)
Whakatauwehea atu te kīanga pātahi 2x-3 mā te whakamahi i te āhuatanga tātai tohatoha.
-2x^{2}-17x+30=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(-17\right)±\sqrt{\left(-17\right)^{2}-4\left(-2\right)\times 30}}{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{-\left(-17\right)±\sqrt{289-4\left(-2\right)\times 30}}{2\left(-2\right)}
Pūrua -17.
x=\frac{-\left(-17\right)±\sqrt{289+8\times 30}}{2\left(-2\right)}
Whakareatia -4 ki te -2.
x=\frac{-\left(-17\right)±\sqrt{289+240}}{2\left(-2\right)}
Whakareatia 8 ki te 30.
x=\frac{-\left(-17\right)±\sqrt{529}}{2\left(-2\right)}
Tāpiri 289 ki te 240.
x=\frac{-\left(-17\right)±23}{2\left(-2\right)}
Tuhia te pūtakerua o te 529.
x=\frac{17±23}{2\left(-2\right)}
Ko te tauaro o -17 ko 17.
x=\frac{17±23}{-4}
Whakareatia 2 ki te -2.
x=\frac{40}{-4}
Nā, me whakaoti te whārite x=\frac{17±23}{-4} ina he tāpiri te ±. Tāpiri 17 ki te 23.
x=-10
Whakawehe 40 ki te -4.
x=-\frac{6}{-4}
Nā, me whakaoti te whārite x=\frac{17±23}{-4} ina he tango te ±. Tango 23 mai i 17.
x=\frac{3}{2}
Whakahekea te hautanga \frac{-6}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
-2x^{2}-17x+30=-2\left(x-\left(-10\right)\right)\left(x-\frac{3}{2}\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 -10 mō te x_{1} me te \frac{3}{2} mō te x_{2}.
-2x^{2}-17x+30=-2\left(x+10\right)\left(x-\frac{3}{2}\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
-2x^{2}-17x+30=-2\left(x+10\right)\times \frac{-2x+3}{-2}
Tango \frac{3}{2} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
-2x^{2}-17x+30=\left(x+10\right)\left(-2x+3\right)
Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te -2 me te 2.