SOLUTION: the product of two consecutive integers is 41 more than their sum. Find the integers.

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Question 172148: the product of two consecutive integers is 41 more than their sum. Find the integers.
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
Call the first integer x. Then the next one can be represented by x+1. Then the product of the two is x(x+1) and "41 more than their sum" can be represented by 41+x+x+1. So
x%28x%2B1%29=41%2Bx%2Bx%2B1
x%5E2%2Bx=42%2B2x
x%5E2-x-42=0
%28x-7%29%28x%2B6%29=0
So x=7 and x=-6. Which one could be correct? Or both? Let's check. If x=7, the other integer is 8, so
7(8)=41+7+8
56=65
And if x=-6 the other integer is -5, so
-6(-5)=41+(-6)+(-5)
30=30
So both are solutions.