SOLUTION: {{{2x^2-3x+1=0}}}Solve by completing the square.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: {{{2x^2-3x+1=0}}}Solve by completing the square.      Log On


   

Question 19275: 2x%5E2-3x%2B1=0Solve by completing the square.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square:
2x%5E2-3x%2B1=0 Divide through by two to make the x^2 coefficient = 1.
x%5E2+-+%283%2F2%29x+%2B+1%2F2+=+0 Now subtract 1/2 from both sides.
x%5E2+-+%283%2F2%29x+=+-1%2F2 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%5E2+-+%283%2F2%29x+%2B+9%2F16+=+9%2F16+-+1%2F2 Simplify and factor the left side.
%28x+-+3%2F4%29%5E2+=+1%2F16 Now take the square root of both sides.
x+-+3%2F4+=+1%2F4 and/or x+-+3%2F4+=+-1%2F4
x+=+3%2F4+%2B+1%2F4 and/or x+=+3%2F4+-+1%2F4
The two roots are:
x = 1
x = 1/2