Question 19275
Solve by completing the square:
{{{2x^2-3x+1=0}}} Divide through by two to make the x^2 coefficient = 1.
{{{x^2 - (3/2)x + 1/2 = 0}}} Now subtract 1/2 from both sides.
{{{x^2 - (3/2)x = -1/2}}} Complete the square in the x-terms by adding the square of half the coefficient of the x-term to both sides. That's (3/4)^2 = 9/16
{{{x^2 - (3/2)x + 9/16 = 9/16 - 1/2}}} Simplify and factor the left side.
{{{(x - 3/4)^2 = 1/16}}} Now take the square root of both sides.
{{{x - 3/4 = 1/4}}} and/or {{{x - 3/4 = -1/4}}}
{{{x = 3/4 + 1/4}}} and/or {{{x = 3/4 - 1/4}}}

The two roots are:

x = 1
x = 1/2