x^2 -2x-1/2 =0" "larr move -1/2 to the other side x^2 -2x " "= 1/2" "larr add color(red)((-2/2)^2) to both sides x^2 -2x " "color(red)(+1)= 1/2 color(red)(+1)
(x-1)^2" "=3/2" "larr write as square of a binomial
x-1" "=+-sqrt(3/2)" "larr find square root of each side
x = +sqrt(3/2)+1" "or x = -sqrt(3/2)+1" "larr solve for x