Question 22674
Let "x" be the number.
It's square is x^2
The average of the number and its square is (x+x^2)/2
Equation:
     x-x^2 = (x+x^2)/2
    2x -2x^2 = x+x^2
     3x^2-x=0
    x(3x-1)=0
  x =0 or x = 1/3
Cheers,
Stan H.