The product of two consecutive negative integers is 600. what is the value of the lesser integer?

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)