How do you solve by completing the square: ##2x^2 + 4x +1 = 0##?

In order to complete the square, add +1 to both sides of the equation:

##2x^2 + 4x + 1 +1 = 0 + 1##; ##2x^2+4x+2=1##; ##2(x^2+2x+1) = 1##; ##x^2+2x+1=1/2##; ##(x+1)^2 = 1/2##; ##x+1 = +-sqrt(1/2) = +-sqrt2 /2##;

Therefore, the answer is :

##x=-1+-sqrt2/2##