# Completing the squares of a multivariable function

1. May 20, 2014

### pondzo

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. May 20, 2014

### SammyS

Staff Emeritus
That looks plenty "nice" to me !