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**