Question 24521
Well, it looks like you were on the right track!
Solve by completing the square:
{{{3x^2-2x+5 = 0}}} First divide through by 3.
{{{x^2-(2/3)x+5/3 = 0}}} Now subtract 5/3 from both sides of the equation.
{{{x^2-(2/3)x = -5/3}}} Complete the square in the x-terms by adding the square of half the x-coefficient {{{(1/3)^2 = 1/9}}} to both sides.
{{{x^2-(2/3)x+1/9 = (1/9)-5/3}}} Factor the left side and simplify.
{{{(x-1/3)^2 = -14/9}}} Take the square root of both sides.
{{{x-1/3 = (1/3)sqrt(14)}}} Add 3 to both sides.
{{{x =3+-sqrt(14)/3}}}