You can put this solution on YOUR website! To find values of c you need values for x, but we can simplify:
x^2+4x+c=0
(x^2+4x)=-c
(x + 2)^2 = 4 - c
4 - (x + 2)^2 = c
The answer for c depends on the value for x. With the information you provided, we can assume that any number can be used for x.... so infinitely many.