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Is there anything wrong with completing the square this way?

  1. May 25, 2012 #1
    3x^2 + 12x + 27
    /3 /3 /3

    3(x^2 + 4x + 9),

    3(x^2 + 4x + 4 + 9 - 4)

    (x^2 + 4x + 4) = (x+2)^2

    3((x + 2)^2 +5)


    This way is different then how it was taught to me but this way makes more sense to me.
     
  2. jcsd
  3. May 25, 2012 #2
    Nope, works just fine. I actually prefer it that way. The idea is that, surely:

    3(x^2 + 4x + 4 + 9 - 4) is equal to 3(x^2 + 4x + 9)

    If you ever have any doubts, expand it out again. If you get the same thing back, you know you're fine.
     
  4. May 25, 2012 #3

    HallsofIvy

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    That is, frankly, the way I have always handled coefficients of [itex]x^2[/itex].
     
  5. May 25, 2012 #4
    Yup that is correct. I wonder what prompted the question.

    I guess the only way that could be incorrect is if a teacher was showing a different method and testing specifically on the knowledge that different method.
     
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