Question 290274
{{{0.5x^2=x+0.5}}} Start with the given equation.



{{{x^2=2x+1}}} Multiply EVERY term by 2 (note: {{{0.5=1/2}}}) to clear out the decimals.



{{{x^2-2x-1=0}}} Get every term to the left side.



*[invoke quadratic_formula 1, -2, -1, "x"]



So the solutions are {{{x=1+sqrt(2)}}} or {{{x=1-sqrt(2)}}}