x= first integer
21-x= second integer
(x)(21-x)= 108
multiply x by each term in parentheses
21x - x^2= 108
subtract 108 from both sides
21x - x^2 - 108= 0
-x^2 + 21x - 108= 0
multiply whole equation by -1 to eliminate the negative coefficient in the first term
(-1)(-x^2 + 21x - 108)= 0
x^2 - 21x + 108= 0
factor (remember we need #s to add to 21 and multiply to 108)
(x-12)(x-9)= 0
x-12= 0
x= 12
x-9= 0
x= 9
CHECK:
9 + 12= 21
9 * 12= 108
ANSWER: The two positive integers that add to 21 and multiply to 108 are 12 and 9.
Hope this helps! :)
