Question 36832
Let the number be x and square of the number be x^2

x + x^2 = 72
x^2 +x -72 = 0
x^2 +9x -8x -72 = 0
x(x+9) -8(x+9) =0 
(x-8)(x+9) = 0

x = 8, -9

Verify
x + x^2
8 +8^2
8 + 64 = 72


x + x^2
(-9) +(-9)^2
-9 + 81 = 72