Solve for P (complex solution)
\left\{\begin{matrix}P=-\frac{x^{2}-6000x+100000}{100y}\text{, }&y\neq 0\\P\in \mathrm{C}\text{, }&\left(x=3000-100\sqrt{890}\text{ or }x=100\sqrt{890}+3000\right)\text{ and }y=0\end{matrix}\right.
Solve for P
\left\{\begin{matrix}P=-\frac{x^{2}-6000x+100000}{100y}\text{, }&y\neq 0\\P\in \mathrm{R}\text{, }&\left(x=3000-100\sqrt{890}\text{ or }x=100\sqrt{890}+3000\right)\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
x=-50\sqrt{-\frac{Py}{25}+3560}+3000
x=50\left(\sqrt{-\frac{Py}{25}+3560}+60\right)
Solve for x
x=-10\sqrt{89000-Py}+3000
x=10\sqrt{89000-Py}+3000\text{, }\left(P\geq 0\text{ or }y\geq \frac{89000}{P}\right)\text{ and }\left(P\leq 0\text{ or }y\leq \frac{89000}{P}\right)
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yP=-\frac{x^{2}}{100}+60x-1000
The equation is in standard form.
\frac{yP}{y}=\frac{-\frac{x^{2}}{100}+60x-1000}{y}
Divide both sides by y.
P=\frac{-\frac{x^{2}}{100}+60x-1000}{y}
Dividing by y undoes the multiplication by y.
P=\frac{-x^{2}+6000x-100000}{100y}
Divide 60x-\frac{x^{2}}{100}-1000 by y.
yP=-\frac{x^{2}}{100}+60x-1000
The equation is in standard form.
\frac{yP}{y}=\frac{-\frac{x^{2}}{100}+60x-1000}{y}
Divide both sides by y.
P=\frac{-\frac{x^{2}}{100}+60x-1000}{y}
Dividing by y undoes the multiplication by y.
P=\frac{-x^{2}+6000x-100000}{100y}
Divide 60x-\frac{x^{2}}{100}-1000 by y.
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