The equation of a circle with center (h,k) and radius r is

(x - h)² + (y - k)² = r²

(h,k) = (-8,-1) and r = 4, so the equation is

(x - 8)² + (y - (-1))² = 4²

(x - 8)² + (y + 1)² = 16

The graph is

 

The x-intercepts are when y=0, so we substitute y=0 in

(x - 8)² + (0 + 1)² = 16
       (x - 8)² + 1 = 16
           (x - 8)² = 15

Use the principles of square roots:

              x - 8 = ±

                  x = 8 ± 

The x-intercepts are 

    (, 0) and (, 0)

which are approximately (4.13,0) and (11.87,0)

Edwin