SOLUTION: The product of two consecutive even integers is 30 more than 9 times the smaller integer. What are the integers?

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Question 196022: The product of two consecutive even integers is 30 more than 9 times the smaller integer. What are the integers?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the smaller even integer be n
The next larger even integer will be n+%2B+2
given:
n%2A%28n+%2B+2%29+=+9n+%2B+30
------------------------
n%5E2+%2B+2n+=+9n+%2B+30
n%5E2+-+7n+-+30+=+0
Using quadratic formula:
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-7
c+=+-30
n+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A%28-30%29+%29%29%2F%282%2A1%29+
n+=+%287+%2B-+sqrt%28+49+%2B+120+%29%29+%2F+2+
n+=+%287+%2B-+13%29+%2F+2+ (I'll ignore the negative root)
n+=+20%2F2
n+=+10
n+%2B+2+=+12
The integers are 10 and 12
check:
n%2A%28n+%2B+2%29+=+9n+%2B+30
10%2A12+=+9%2A10+%2B+30
120+=+90+%2B+30
120+=+120
OK