The sum of a number and its square is 72. find the number.

The sum  of a number, n, and its square n^2 is 72. In equation form, this is n + n^2 = 72. Try making this into a polynomial equaling 0.
n + n^2 =72       subtract 72
n^2 + 1n -72 = 0        Now factor this polynomial
(n-8) (n+9)  = 0 Solutions to this problem are 8 and -9
Plug in for n to check.
 8 + 64 = 72        8 is correct
 -9 + 81 =  72      -9  is also correct!!

Neither is the answer