Solve (x-40)^2=p+1600

$$( x - 40 ) ^ { 2 } = p + 1600$$

Solve for p

$$p=x\left(x-80\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-40\right)^{2}.

$$x^{2}-80x+1600=p+1600$$

Swap sides so that all variable terms are on the left hand side.

$$p+1600=x^{2}-80x+1600$$

Subtract 1600 from both sides.

$$p=x^{2}-80x+1600-1600$$

Subtract 1600 from 1600 to get 0.

$$p=x^{2}-80x$$

Solve for x (complex solution)

$$x=-\sqrt{p+1600}+40$$

$$x=\sqrt{p+1600}+40$$

Solve for x

$$x=-\sqrt{p+1600}+40$$

$$x=\sqrt{p+1600}+40\text{, }p\geq -1600$$