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Rational Completeing the Square

  1. Feb 3, 2013 #1

    ISX

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    1. The problem statement, all variables and given/known data
    51v52u.jpg


    2. Relevant equations
    9fxswl.jpg

    3. The attempt at a solution
    Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.
    2ivzmoj.jpg
     
  2. jcsd
  3. Feb 3, 2013 #2

    SammyS

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    Your line

    [itex]\displaystyle x^2-\frac{5}{6}x+\frac{25}{144}=-\frac{1}{6}+\frac{25}{144}[/itex]

    is correct.

    What your last line shows (correctly) is that [itex]\displaystyle \left(x-\frac{5}{6}\right)^2\ne x^2-\frac{5}{6}x+\frac{25}{144}\ .[/itex]

    When you square 5/6, you don't get 25/144 .

    How did you get 25/144 in the first place? You squared 5/12 not 5/6 .
     

    Attached Files:

  4. Feb 3, 2013 #3
    you went from
    [itex]x^2 +bx + (\frac{b}{2})^{2}[/itex]
    to
    [itex](x+b)^{2}[/itex]

    and not to

    [itex](x+\frac{b}{2})^{2}[/itex]
     
  5. Feb 3, 2013 #4

    ISX

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    Hellllllll I've been doing it wrong for centuries then. Lets try this again.

    2exspdu.jpg

    2128lz5.jpg

    Ahhhh! Thanks for the help guys! I was always just dropping the last number off and went with the first 2. Guess I never caught on that fractions didnt work that way.
     
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