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Quadratic equation thingy

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data

    Given that for all values of x:

    3x^2 + 12x + 5 = p(x +q)^2 + r

    a) find the values of p, q and r
    b) solve the equation 3x^2 + 12x + 5 = 0

    3. The attempt at a solution

    I'm completely lost here but here's my attempt at a solution - I'm pretty sure that I did it all wrong:

    I divided them by 3 and moved the last bit to the other side of the equal sign and made it a minus. I tried using the complete the square method:


    After that I have no idea what to do... I don't have a clue how I find the values of p, q and r.
  2. jcsd
  3. Sep 21, 2010 #2


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    Homework Helper

    Try to rewrite [tex] 3x^2 + 12x +5 [/tex] itself using completing the square, then compare the result to [tex] p(x+q)^2 + r [/tex]
  4. Sep 21, 2010 #3
    I'm sorry you have to be more clear, I'm a newb.
  5. Sep 21, 2010 #4


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    In other words, don't divide by 3 first. It is possible to complete the square even if the coefficient of the x2 term is not 1. Here's a hint to get you started: factor out a GCF from the first 2 terms only (ignoring the constant term).
  6. Sep 21, 2010 #5


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    Start with [itex] 3x^2+12 + 5 [/itex], write it as [itex] 3(x^2+4x) + 5 [/itex], and complete the square to write it as [itex] 3(x+ \text{something })^2 + \text{something}[/itex].

    Then compare it with [itex] p(x+q)^2 + r [/itex].
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