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Math Help - quadratic problem

  1. #1
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    quadratic problem

    x^2 - 14x + a = (x + b)^2

    for all values of x, ive been asked to find the value of a and the value of b

    im not sure, but i think the solution to this may lie in 'completing the square'.

    (x-7)^2 - 49 + a = (x + \frac{2b}{2})^2 - \frac{4b^2}{4} + b^2

    i think i was going round in circles

    x^2 -14x + 49 - 49 + a = x^2 + 2bx + \frac{4b^2}{4} - \frac{4b^2}{4} + b^2 expanding the above
    x^2 -14x + a = x^2 + 2bx + b^2 simplify
    -14x + a=2bx + b^2 and cancel
    Last edited by sammy28; February 26th 2009 at 07:19 AM.
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  2. #2
    MHF Contributor red_dog's Avatar
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    x^2-14x+a=x^2+2bx+b^2

    Then, \left\{\begin{array}{ll}2b=-14\\b^2=a\end{array}\right.

    Now, solve the system.
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  3. #3
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    thanks for that, should have stepped back a bit before trying it
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