Question

Find all of the points on the x-axis which are 6 units from the point (−1, 1).

Answer 1

All the points that are 6 units from (-1, 1) are those on the circle
  (x+1)^2 +(y-1)^2 = 36

For y=0, the two points of interest satisfy
  (x+1)^2 +1 = 36
  (x+1)^2 = 35 . . . . . . subtract 1
  x+1 = ±√35
  x = -1±√35

The points you seek are (-1-√35, 0) and (-1+√35, 0), about (-6.916, 0) and (4.916, 0).