Solve A=(x+1)^2-4

$$A = ( x + 1 ) ^ { 2 } - 4$$

Solve for A

$$A=\left(x-1\right)\left(x+3\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$A=x^{2}+2x+1-4$$

Subtract 4 from 1 to get -3.

$$A=x^{2}+2x-3$$

Solve for x (complex solution)

$$x=-\left(\sqrt{A+4}+1\right)$$

$$x=\sqrt{A+4}-1$$

Solve for x

$$x=-\left(\sqrt{A+4}+1\right)$$

$$x=\sqrt{A+4}-1\text{, }A\geq -4$$