Solve B=(-x-5)^2-25

$$B = ( - x - 5 ) ^ { 2 } - 25$$

Solve for B

$$B=x\left(x+10\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-x-5\right)^{2}.

$$B=\left(-x\right)^{2}-10\left(-x\right)+25-25$$

Calculate -x to the power of 2 and get x^{2}.

$$B=x^{2}-10\left(-x\right)+25-25$$

Multiply -10 and -1 to get 10.

$$B=x^{2}+10x+25-25$$

Subtract 25 from 25 to get 0.

$$B=x^{2}+10x$$

Solve for x (complex solution)

$$x=-\left(\sqrt{B+25}+5\right)$$

$$x=\sqrt{B+25}-5$$

Solve for x

$$x=-\left(\sqrt{B+25}+5\right)$$

$$x=\sqrt{B+25}-5\text{, }B\geq -25$$