Solve P=4000-40(x-25)^2

$$P = 4000 - 40 ( x - 25 ) ^ { 2 }$$

Solve for P

$$P=40\left(15-x\right)\left(x-35\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-25\right)^{2}.

$$P=4000-40\left(x^{2}-50x+625\right)$$

Use the distributive property to multiply -40 by x^{2}-50x+625.

$$P=4000-40x^{2}+2000x-25000$$

Subtract 25000 from 4000 to get -21000.

$$P=-21000-40x^{2}+2000x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{40000-10P}}{20}+25$$

$$x=\frac{\sqrt{40000-10P}}{20}+25$$

Solve for x

$$x=-\frac{\sqrt{40000-10P}}{20}+25$$

$$x=\frac{\sqrt{40000-10P}}{20}+25\text{, }P\leq 4000$$