Question 27967
x^2 + 6x + 13 = 0
x^2 + 2X(3)(x) + (9+4) = 0  
[x^2 + 2X(x)X(3)+ 3^2] +4= 0  
(notice a form a^2+2ab +b^2 in the LHS  with a= x and b=3)
(x+3)^2 =-4
(x+3)^2 = (2i)^2
(x+3) = + or - (2i)
x+ 3 = 2i or x+ 3 = -2i
That is x =(2i-3) and x = -2i-3 =-(2i+3)  
Abswer: x =(2i-3)  and x = -(2i+3)