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Math Help - complete squares

  1. #1
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    complete squares

    Hi there. I need to know where is my mistake so I can correct it. Hope you can help me.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    The problem is that a^2+5a+1^2 is not a perfect square. A perfect square is something like x^2+2xy+y^2=(x+y)^2. If you choose x=a and y=1, the term 2xy equals 2a, not 5a... it doesn't work.
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  3. #3
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    Quote Originally Posted by Alienis Back View Post
    Hi there. I need to know where is my mistake so I can correct it. Hope you can help me.
    Unfortunately you made a mistake when factorizing

    a^2+5a+1 = \underbrace{a^2+5a+{\bold{\color{red}\dfrac{25}4 - \dfrac{25}4}} + 1}_{completing\ the\ square} = \underbrace{\left(a+\dfrac52\right)^2-\dfrac{21}4}_{sum\ of\ squares} = \underbrace{\left[\left(a+\dfrac52\right)+\sqrt{\dfrac{21}4}\right] \left[\left(a+\dfrac52\right)-\sqrt{\dfrac{21}4}\right]}_{factorized}

    And now go ahead!
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