Solve for P
P=-\frac{x^{2}}{10}+70x+5000
Solve for x (complex solution)
x=5\sqrt{-\frac{2P}{5}+6900}+350
x=-5\sqrt{-\frac{2P}{5}+6900}+350
Solve for x
x=\sqrt{172500-10P}+350
x=-\sqrt{172500-10P}+350\text{, }P\leq 17250
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P=100x-0.1x^{2}-\left(30x-5000\right)
Use the distributive property to multiply x by 100-0.1x.
P=100x-0.1x^{2}-30x+5000
To find the opposite of 30x-5000, find the opposite of each term.
P=70x-0.1x^{2}+5000
Combine 100x and -30x to get 70x.
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