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Homework Help: Putting an equation in quadratic form

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Could someone please explain how to go about putting an equation in to quadratic form.
    e.g:
    Q(x,y,z)=7x^2-2y^2-40z^2-14xz+20yz.

    2. Relevant equations



    3. The attempt at a solution

    I know it equals 7(x-z)^2 -2(y-5z)^2 +3z^2. dnt know how to get there though
     
  2. jcsd
  3. Apr 28, 2010 #2

    Mentallic

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    Homework Helper

    Firstly look at [tex]7x^2-14xz[/tex]

    This becomes [tex]7(x^2-2xz)[/tex] and now you just need to complete the square on that factor. Remember to subtract whatever you added to complete the square.

    [tex]7(x^2-2xz+z^2)-7z^2[/tex]

    [tex]7(x-z)^2-7z^2[/tex]

    Now do this for the other two terms as well.
     
  4. Apr 28, 2010 #3
    Thanks that helped. I can do them now.
     
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