Question 202878
Since the difference between the 2 numbers is – 8, it means that the larger number is subtracted from the smaller number to get – 8. By letting the smaller number be s, and the larger number l, we have the following equations:


s – l = - 8 
sl = 20


Using the 1st equation to solve for l, we get:   

-	l = - 8 – s
l  =  8  +  s


Substituting this value, 8 + s for l in equation 2, we get: 

s(8 + s) = 20
{{{s^2+8s-20=0}}}
(s + 10)(s – 2)  =  0


s = {{{highlight(-10)}}}, or {{{highlight(2)}}}


Therefore, s, or the smaller number can either be – 10, or 2


If the small number is – 10, then the larger number is - 2


Check
s – l = - 8
- 10 - - 2 =  - 8
- 10 +  2 = - 8 (TRUE)


sl = 20
- 10 * - 2 = 20 (TRUE)


If the small number is 2, then the larger number is 10


Check
s  - l = - 8
2 – 10 = - 8 (TRUE)


sl = 20
2 * 10 = 20 TRUE)