Solve B=9-(2-x)^2

$$B = 9 - ( 2 - x ) ^ { 2 }$$

Solve for B

$$B=-\left(x-5\right)\left(x+1\right)$$

Solution Steps

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

$$B=9-\left(4-4x+x^{2}\right)$$

To find the opposite of 4-4x+x^{2}, find the opposite of each term.

$$B=9-4+4x-x^{2}$$

Subtract 4 from 9 to get 5.

$$B=5+4x-x^{2}$$

Solve for x (complex solution)

$$x=\sqrt{9-B}+2$$

$$x=-\sqrt{9-B}+2$$

Solve for x

$$x=\sqrt{9-B}+2$$

$$x=-\sqrt{9-B}+2\text{, }B\leq 9$$