Completing the Square - Math Help Needed!

Discussion in 'Community Discussion' started by psycoswimmer, Nov 8, 2009.

  1. psycoswimmer macrumors 65816

    psycoswimmer

    Joined:
    Sep 27, 2006
    Location:
    USA
    #1
    So, I've been trying to figure out this problem for a while and I can't figure out how to do it. The question states: "Solve 2x^2 - 12x + 4 = 0 by completing the square, expressing the result in simplest radical form." I'm not sure how to continue with completing the square with a leading coefficient... I tried pulling out a 2 but then got confused up to the point were I had (2)(x+3)^2=7.

    Any help is greatly appreciated!
     
  2. AngryApple macrumors 6502

    Joined:
    Dec 25, 2008
    #2
    I don't know if I did it right:

    x = 3 + root 7
     
  3. fireshot91 macrumors 601

    fireshot91

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    Jul 31, 2008
    Location:
    Northern VA
    #3
    My first bet would be to factor it, making it 2(x^2-6x+2)=0, but that leads you nowhere, since you can't factor that anymore.
     
  4. sammich macrumors 601

    sammich

    Joined:
    Sep 26, 2006
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    Sarcasmville.
    #4
    Your first step is to get the coeff of x^2 to be equal to 1

    Stepwise:

    .x² - 6x + 2 = 0............after dividing by 2
    (x² - 6x + 9) + 2 . 9 = 0...complete the square: add (b/2)² = 9
    (x - 3)² = 7................solving for x
    .x - 3...= √7
    .x.......= -3 - √7
     
  5. imaketouchtheme macrumors 65816

    Joined:
    Dec 5, 2007
    #5
    Ok, when there's a coefficient in front of the x^2, you have to first divide the entire equation by the coefficient, which will look like this:

    x^2-6x+2=0

    All I did was divide everything by 2.

    After that, move your "c" term over (since the equation is in the form of ax^2-bx+c=0)

    Now you have x^2-6x=-2

    If you need anymore help from there, let me know. :)
     
  6. Tomorrow macrumors 604

    Tomorrow

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    #6
    Fixed. You were close. Remember, a quadratic equation can have two roots, often related to the positive and negative roots of (b^2-4ac). It's a good idea to check your work using the quadratic formula.
     
  7. sammich macrumors 601

    sammich

    Joined:
    Sep 26, 2006
    Location:
    Sarcasmville.
    #7
    Oh man, bad memories of little mistakes in maths exams.

    Thanks for fixing those up for me. And to think, I'm studying engineering :D
     
  8. Tomorrow macrumors 604

    Tomorrow

    Joined:
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    #8
    You poor soul. (spoken by a 40-year-old engineer)

    ;)
     
  9. psycoswimmer thread starter macrumors 65816

    psycoswimmer

    Joined:
    Sep 27, 2006
    Location:
    USA
    #9
    Thanks everyone, I finally got it. And yes, the answer is 3 ± √7. :)
     

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