The equation x^2 + ax = -14 - 6 - 8x has only integer solutions for x. If a is a positive integer, what is the greatest possible value of a?
Rearrange as
x^2 + (a + 8)x + 20 = 0
Note that 20 =
4 * 5
2 *10
1 * 20
So
(x + 4) ( x + 5) = x^2 + 9x + 20 and a =1
(x +2)( x +10) =x^2 + 12x + 20 and a = 4
(x + 20) ( x + 1) = x^2 + 21x + 20 and a = 13
