Solve y=(x+3)^2-4

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

Solve for y

$$y=\left(x+1\right)\left(x+5\right)$$

Solution Steps

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

$$y=x^{2}+6x+9-4$$

Subtract 4 from 9 to get 5.

$$y=x^{2}+6x+5$$

Solve for x (complex solution)

$$x=-\left(\sqrt{y+4}+3\right)$$

$$x=\sqrt{y+4}-3$$

Solve for x

$$x=-\left(\sqrt{y+4}+3\right)$$

$$x=\sqrt{y+4}-3\text{, }y\geq -4$$