SOLUTION: If 5 is added to a number, the result is the same as that obtained by multiplying it reciprocal by 14. What is the number?

Question 27822: If 5 is added to a number, the result is the same as that obtained by multiplying it reciprocal by 14. What is the number?
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
If 5 is added to a number (5+x), the result is the same as (equals) that obtained by multiplying its reciprocal (1/x) by 14 (times 14). What is the number?

Multiply all terms by x:
Rearrange:
Solving by completing the square (adding (5/2)^2 to both sides):

(Ignore the 0, just makes the equation editor work)
(Again, ignore the 0)

So x = =2 or =-7
If 5 is added to 2, the result (7) is the same as its reciprocal (1/2) multiplied by 14 (1/2*14=7) Check.
If 5 is added to -7 the result (-2) is the same as its reciprocal (-1/7) multiplied by 14 (-1/7*14=-2) Check.
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