Center and radius of circle.

Alright so it says find the center and radius of THIS :

$\displaystyle x^2 + y^2 + x = 0$

Somehow they got numbers that WERENT variables in there

(Moved the x's together and put them in brackets) Like this :

$\displaystyle (x^2 + x) + y^2$

(Then put these in)

$\displaystyle (x^2 + x + {1\over 4} - {1\over 4}) + y^2$

What the HELL did they do to be able to do that? Like it cancels out so can i put whatever numbers i want in there as long as they equal 0 or something? In that case wouldnt using 1 make it easier?

Any explainations?

Can post next steps of the answer if anyone would like