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3x^2 - 5x - 1 = 0 (Solve using completing the square method)

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Question: 3x^2 - 5x - 1 = 0 (Solve using completing the square method)


    2. Relevant equations



    3. The attempt at a solution
    3x^2 - 5x - 1 = 0
    x^2 - (5/3)x - 1/3 = 0
    x^2 - (5x/3) = 1/3
    x^2 - 2(5x/3) = 1/3
    x^2 - 2(5x/3) + (5/6)^2 = 1/3 + (5/6)^2
    (x - 5/6)^2 = 1/3 + 25/36
    (x - 5/6)^2 = 37/36
    x - 5/6 = + - Square root 37/36
    x = Square root 37/36 + 5/6 or x = - Square root 37/36 + 5/6
    x = 1.85 (3sf) or x = -0.180 (3sf)

    I am sorry if the working is messy! I can't find the appropriate key for it
    Please check my answer and correct me

    Thank you!!!!!
     
  2. jcsd
  3. Jan 29, 2012 #2

    Mentallic

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    Homework Helper

    How did you get from the first to the second? What you basically said here is that if

    [itex]a+b=c[/itex]

    then

    [itex]a+2b=c[/itex]

    This is not true unless b=0, which is not the case. What you should have instead done is

    [itex]a+b=c[/itex]

    then

    [itex]a+2(\frac{b}{2})=c[/itex]

    Notice here that nothing has changed, so the equality still holds.

    Everything else seems good and you have the correct answer :smile:
     
  4. Jan 29, 2012 #3

    Thanks for taking the time to check!

    Edit: It should has been x^2 - 2(5x/6) = 1/3
    x^2 - 2(5x/6) + (5/6)^2 = 1/3 + (5/6)^2
     
  5. Jan 29, 2012 #4

    Mentallic

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    Homework Helper

    Yep that's better!
     
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