SOLUTION: The product of two consecutive positive integers is 12 more than 5 times the smaller integer. Find the integers.

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Question 965000: The product of two consecutive positive integers is 12 more than 5 times the smaller integer. Find the integers.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x=smaller integer; x+1=larger integer
%28x%29%28x%2B1%29=5x%2B12
x%5E2%2Bx=5x%2B12 Subtract 5x from each side.
x%5E2-4x=12 Subtract 12 from each side.
x%5E2-4x-12=0
%28x-6%29%28x%2B2%29=0
x-6=0 or x%2B2=0
x=6 or x=-2
ANSWER 1: The smaller integer is 6.
x%2B1=6%2B1=7 ANSWER 2: The larger integer is 7.
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CHECK:
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%28x%29%28x%2B1%29=5x%2B12
%286%29%287%29=5%286%29%2B12
42=30%2B12
42=42