Question 102876
The left side is a perfect square trinomial, which makes this work this way:

{{{x^2 + 4x + 4 = 7 }}}
{{{(x+2)^2 = 7}}}


Next, take the square root of each side:
{{{x+2= 0+-sqrt(7) }}}


Finally, subtract 2 from each side:
{{{x=-2+-sqrt(7) }}}


R^3 
Dr. Robert Rapalje, Retired