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Determining the equation of a 3d sphere

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data
    The question is describe the surface whose equation is given
    2x^2 +2y^2 + 2z^2 - 2x -3y +5z -2 = 0
    now I know it needs to be grouped like this
    (2x^2-2x) + (2y^2-3y) + (2z^2+5z)=2,
    however from here I feel like I am forgetting some kind of basic algebra or something on how to factor this. Kind of stupid I know :/ Can someone please point me in the right direction?
     
  2. jcsd
  3. Sep 11, 2011 #2

    LCKurtz

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    Complete the squares on all three variables.
     
  4. Sep 11, 2011 #3
    thats what I thought but how would it work in this situation, especially since you have the coefficients out on the first term?
     
  5. Sep 11, 2011 #4

    LCKurtz

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    If you have something like 3x2+5x - 1, it is best to factor out the leading coefficient before completing the square:

    [tex]3x^2 +5x -1 = 3(x^2+\frac 5 3 x - \frac 1 3)[/tex]

    and complete the square inside the parentheses:

    [tex]3\left((x^2 +\frac 5 3 x + \frac {35}{36} + (-\frac 1 3 - \frac {35}{36})\right)
    =3\left((x+\frac 5 6)^2-\frac{47}{36}\right)[/tex]
     
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