Two consecutive negative integers are n and n+1. We are told that the product of these two integers is 600 so:
n(n+1)=600
n^2+n=600
n^2+n-600=0
n^2+25n-24n-600=0
n(n+25)-24(n+25)=0
(n-24)(n+25)=0, since we are told that n is negative...
n=-25
(...-25(-24)=600 so -25 is the value of the lesser integer)
