SOLUTION: Six times a number added to twice the reciprocal of a number equals 13. Find the number(s).

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Question 291619: Six times a number added to twice the reciprocal of a number equals 13. Find the number(s).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the unknown number
given:
6n+%2B+2%2A%281%2Fn%29+=+13
Multiply both sides by n
6n%5E2+%2B+2+=+13n
6n%5E2+-+13n+%2B+2+=+0
Solve using quadratic formula
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+6
b+=+-13
c+=+2
n+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A6%2A2+%29%29%2F%282%2A6%29+
n+=+%2813+%2B-+sqrt%28169+-+48+%29%29%2F12+
n+=+%2813+%2B-+sqrt%28121+%29%29%2F12+
n+=+%2813+%2B-+11%29%2F12
The solutions are:
n+=+%2813+%2B+11%29%2F12
n+=+2
and
n+=+%2813+-+11%29%2F12
n+=+1%2F6
Both these solutions work if you plug them
back into 6n+%2B+2%2A%281%2Fn%29+=+13