Solve R=10,000-(x-20)^2

$$R = 10,000 - ( x - 20 ) ^ { 2 }$$

Solve for R

$$R=-\left(x-120\right)\left(x+80\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-20\right)^{2}.

$$R=10000-\left(x^{2}-40x+400\right)$$

To find the opposite of x^{2}-40x+400, find the opposite of each term.

$$R=10000-x^{2}+40x-400$$

Subtract 400 from 10000 to get 9600.

$$R=9600-x^{2}+40x$$

Solve for x (complex solution)

$$x=-\sqrt{10000-R}+20$$

$$x=\sqrt{10000-R}+20$$

Solve for x

$$x=-\sqrt{10000-R}+20$$

$$x=\sqrt{10000-R}+20\text{, }R\leq 10000$$