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Homework Help: Completing the squares of a multivariable function

  1. May 20, 2014 #1
    1. The problem statement, all variables and given/known data

    completing the squares; ## x^2+y^2+2xy-2x-2y+43 = 0##

    3. The attempt at a solution

    I did it as follows, but i would like to know if there is a different 'nicer' method to complete it;

    ## x^2 + y^2 + 2xy − 2x − 2y + 43 ##

    ## = (x + y)^2 − 2x − 2y + 43 ##

    ## = (x + y)^2 − 2(x + y) + 43 ##

    ## = (x + y)^2 − 2(x + y) + 1 + 42 ##

    ## = ((x + y) − 1)^2 + 42 ##
     
  2. jcsd
  3. May 20, 2014 #2

    SammyS

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    That looks plenty "nice" to me !
     
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