Question

Find all solutions of the equation x^2 -2 x + 6 = 0 by completing the square. Express the soutions in the form a + b i:

Answer 1

$x^2-2x+6=0\\ x^2-2x+1+5=0\\ (x-1)^2=-5\\ x-1=\sqrt{-5} \vee x-1=-\sqrt{-5}\\ x=1+5i \vee x=1-5i$