Completing the squares of a multivariable function

[pondzo]

Homework Statement

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

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;

$x^2 + y^2 + 2xy − 2x − 2y + 43$

$= (x + y)^2 − 2x − 2y + 43$

$= (x + y)^2 − 2(x + y) + 43$

$= (x + y)^2 − 2(x + y) + 1 + 42$

$= ((x + y) − 1)^2 + 42$

 

[SammyS]

Homework Statement

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

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;

$x^2 + y^2 + 2xy − 2x − 2y + 43$

$= (x + y)^2 − 2x − 2y + 43$

$= (x + y)^2 − 2(x + y) + 43$

$= (x + y)^2 − 2(x + y) + 1 + 42$

$= ((x + y) − 1)^2 + 42$

That looks plenty "nice" to me !