Answer:
 4 meters
Step-by-step explanation:
If the path has width w meters, the overall dimensions of the pool area are ...
 (18+2w) by (28+2w)
so the overall area in square meters is ...
 (18 +2w)(28 +2w) = 936
 4w² + 92w -432 = 0 . . . . . subtract 936 and eliminate parentheses
 w² + 23w -108 = 0 . . . . . . . divide by 4
 (w +27)(w -4) = 0 . . . . . . . . factor
The positive solution to this equation is w = 4.
The width of the path is 4 meters.
