SOLUTION: Help. The sum of half a number and its reciprocal is the same as 51 divided by the number. Find the number.

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Question 29336: Help. The sum of half a number and its reciprocal is the same as 51 divided by the number. Find the number.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be x
Half a number = x/2
Recipocal = 1/x
Equation:
x%2F2%2B1%2Fx=51%2Fx --> multiply the whole equation by x
x%5E2%2F2%2B1=51----> multply the whole eqaution by 2
2%28x%5E2%2F2%29%2B2%281%2F1%29=2%28102%2F1%29
x%5E2%2B2=102
x%5E2=100
x%5E2=sqrt%28100%29
x=10

Hence, the number is 10.
Paul.