SOLUTION: The product of two consecutive negative integers is 89 more than the their sum. Find the larger interger.

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Question 249021: The product of two consecutive negative integers is 89 more than the their sum. Find the larger interger.
Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = negative number
Let x-1 = consecutive negative number

x%28x-1%29=89%2Bx%2Bx-1
x%5E2-x=88%2B2x
x%5E2-x-2x-88=0
x%5E2-3x-88=0
%28x-11%29%28x%2B8%29=0
Possible solutions: x=11 and x=-8

Let's see which answer fits our original problem:

x%28x-1%29=89%2Bx%2Bx-1
11%2811-1%29=89%2B11%2B11-1
11%2810%29=110
110=110 <--- answer checks when x=110 and x-1=109.
However, even though it checks, it does not apply to our problem
because we are looking for negative consecutive numbers.

Let's try the other one:
x%28x-1%29=89%2Bx%2Bx-1
-8%28-8-1%29=89%2B%28-8%29%2B%28-8%29-1
-8%28-9%29=72
72=72 <--- this answer checks and the solution set contains negative numbers!!
Solution set: x= -8, -9