SOLUTION: Please show me how to solve this problem by completing the square. {{{3x^2-2x+5=0}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please show me how to solve this problem by completing the square. {{{3x^2-2x+5=0}}}      Log On


   

Question 24521: Please show me how to solve this problem by completing the square. 3x%5E2-2x%2B5=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, it looks like you were on the right track!
Solve by completing the square:
3x%5E2-2x%2B5+=+0 First divide through by 3.
x%5E2-%282%2F3%29x%2B5%2F3+=+0 Now subtract 5/3 from both sides of the equation.
x%5E2-%282%2F3%29x+=+-5%2F3 Complete the square in the x-terms by adding the square of half the x-coefficient %281%2F3%29%5E2+=+1%2F9 to both sides.
x%5E2-%282%2F3%29x%2B1%2F9+=+%281%2F9%29-5%2F3 Factor the left side and simplify.
%28x-1%2F3%29%5E2+=+-14%2F9 Take the square root of both sides.
x-1%2F3+=+%281%2F3%29sqrt%2814%29 Add 3 to both sides.
x+=3%2B-sqrt%2814%29%2F3