Question 152194
Let the number be n, then the next higher number is n + 1
The sum of the number and its square can be written as n + n^2.
Twelve times the next higher number can be expressed as 12(n + 1).
As the sum of the number and its square is twelve times the next higher number, we have:
n + n^2 = 12(n + 1)
Solving the quadratic equation for x, we have
n + n^2 = 12n + 12
n^2 - 11n - 12 = 0
(n - 12)(n + 1) = 0
So n = 12 or n = -1
Therefore the number is 12 or -1.