Question 763687
Your steps are in the wrong direction.  The given equation is in a form easy to solve for x.  Trying to factor, or trying to put into general form is counter productive.  Just solve for x without any tricks.  Do you see, just by looking at the equation, the solution will contain imaginary numbers?  


{{{(x+2)^2=-7}}}
{{{((x+2)^2)^(1/2)=(-7)^(1/2)}}}
{{{(x+2)=0+- sqrt(-7)}}}
{{{x=-2+- sqrt(-7)}}}


Using {{{i^2=-1}}},
{{{highlight(x=2+- i*sqrt(7))}}}