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Math Help - an algebra question

  1. #1
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    Sep 2005
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    an algebra question

    hello.

    i have got this one algebra question for homework.

    however i had no idea on how to do this attached one.

    i need to find answers for both a= and b=.
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  2. #2
    MHF Contributor
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    One way is to expand the righthand side, then match its terms to those of the lefthand side.

    x^2 +6x -3 = (x+a)^2 +b
    x^2 +6x -3 = (x^2 +2ax +a^2) +b
    x^2 +6x -3 = x^2 +2ax +a^2 +b
    x^2 +6x -3 = x^2 +2ax +(a^2 +b)

    So,
    x^2 = x^2 ----(i)
    6x = 2ax -----(ii)
    -3 = (a^2 +b) -----(iii)

    From (ii),
    6 = 2a
    a = 6/2 = 3 ----***

    Substitute that into (iii),
    -3 = (3)^2 +b
    -3 = 9 +b
    -3 -9 = b
    b = -12 ---***

    Check those in the original equation,
    x^2 +6x -3 = (x+a)^2 +b
    x^2 +6x -3 =? (x+3)^2 +(-12)
    x^2 +6x -3 =? (x^2 +6x +9) -12
    x^2 +6x -3 =? x^2 +6x +9 -12
    x^2 +6x -3 =? x^2 +6x -3
    Yes, so, OK

    Therefore, a = 3 and b = -12. -------answer.
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  3. #3
    Member
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    Sep 2005
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    thank you.

    u have given me an excellent description. thanks.
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