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Math Help - I'm not sure what this topic is called?

  1. #1
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    I'm not sure what this topic is called?

    My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

    Heres the question:

    given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

    Any help appreciated
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by nickboi View Post
    My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

    Heres the question:

    given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

    Any help appreciated
    Hello nickboi,

    This exercise has to do with "completing the square". With a quadratic and linear term given, what constant would you have to add in order for that to become a perfect square trinomial. Then, your perfect square trinomial becomes a binomial squared.
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  3. #3
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    Thanks for the help. But im not quite sure what you mean by "Then, your perfect square trinomial becomes a binomial squared."
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  4. #4
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    Go ahead and multiply out the right side:
    x^2- 14x+ a= x^2+ 2b+ b^2
    In order that those be the same for all x, you must have the same coefficients: -14= 2b and a= b^2.

    As masters said, that is basically "completing the square".
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  5. #5
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    Thanks you two, i'll give that a try and post my success.
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  6. #6
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    It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.
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  7. #7
    A riddle wrapped in an enigma
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    Quote Originally Posted by nickboi View Post
    It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.
    Right back at ya!
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