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!