Find $a^2 + b^2+c^2$ Given 
$a^2+2b = 7$
$b^2+4c = -7$
$c^2+6a = -14$
Find $a^2 + b^2 + c^2$
The answer was an Integer
I tried to solve it by making $a$ the subject of the equation and substituting in others but equations became too complex(got $a^8$!) and difficult to solve.

HINT:
Completing the square, 
$$(a+3)^2+(b+1)^2+(c+2)^2=7-7-14+9+1+4=0$$
Now if $a,b,c$ are real, what can we derive from here? 
