We have to solve x^2 +2x+5=0 by completion of squares.
We use the relation x^2 + 2xy + y^2 = (x + y)^2
x^2 +2x+5=0
=> x^2 + 2x*1 + 1^2 + 4 = 0
=> (x + 1)^2 + 4 = 0
=> (x + 1)^2 = -4
=> x + 1 = 2i and x + 1 = -2i
=> x = -1 + 2i and x = -1 - 2i
The solution of the equation is x = -1 + 2i and x = -1 - 2i