Solve B=(4x+3)^2-16

$$B = ( 4 x + 3 ) ^ { 2 } - 16$$

Solve for B

$$B=\left(4x-1\right)\left(4x+7\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+3\right)^{2}.

$$B=16x^{2}+24x+9-16$$

Subtract 16 from 9 to get -7.

$$B=16x^{2}+24x-7$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{B+16}-3}{4}$$

$$x=\frac{\sqrt{B+16}-3}{4}$$

Solve for x

$$x=\frac{-\sqrt{B+16}-3}{4}$$

$$x=\frac{\sqrt{B+16}-3}{4}\text{, }B\geq -16$$