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9\left(-p^{2}+2000p\right)
Tauwehea te 9.
p\left(-p+2000\right)
Whakaarohia te -p^{2}+2000p. Tauwehea te p.
9p\left(-p+2000\right)
Me tuhi anō te kīanga whakatauwehe katoa.
-9p^{2}+18000p=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.
p=\frac{-18000±\sqrt{18000^{2}}}{2\left(-9\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.
p=\frac{-18000±18000}{2\left(-9\right)}
Tuhia te pūtakerua o te 18000^{2}.
p=\frac{-18000±18000}{-18}
Whakareatia 2 ki te -9.
p=\frac{0}{-18}
Nā, me whakaoti te whārite p=\frac{-18000±18000}{-18} ina he tāpiri te ±. Tāpiri -18000 ki te 18000.
p=0
Whakawehe 0 ki te -18.
p=-\frac{36000}{-18}
Nā, me whakaoti te whārite p=\frac{-18000±18000}{-18} ina he tango te ±. Tango 18000 mai i -18000.
p=2000
Whakawehe -36000 ki te -18.
-9p^{2}+18000p=-9p\left(p-2000\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 0 mō te x_{1} me te 2000 mō te x_{2}.