minimum

Completing the square on $x$ and $y$ independently to write the given expression as
$(x+a)^2+(y+b)^2+c$.   The answer is $c$.
 

Put into standard circle form :

(x +1)^2   +  (y-5.5)^2   = -8 +1+ 30.25              r = sqrt 23.25     center = -1, 5.5     

Minumum 'x'   will be     - 1 - sqrt 23.25

Minumum 'y' will be         5.5 - sqrt 23.5       (check my math)