SOLUTION: One negative integer is 5 less than another, and their product is 84. Find the integers. I know the answer is -12 X -7. But how do I find the equation to solve this problem?

Question 247231: One negative integer is 5 less than another, and their product is 84. Find the integers.
I know the answer is -12 X -7.
But how do I find the equation to solve this problem?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
let -n= first integer and -m the second
-n=-m-5
-n(-m)=84
substitute
(-m-5)(-m)=84
m^2+5m=84
complete the square
add (5/2)^2 to both sides
m^2+5m+15/4=84+15/4
m^2+5m+15/4=361/4
factor
(m+5/2)^2=361/4
get sqrt
m+5/2=+\-19/2
m=-5/2+\-19/2
m=-24/2=-12
m=14/2=7
since we want a negative integer it can't be 7
so we have -12
-12+5=-7

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