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?

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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) About Me  (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?
5%2Bx=%281%2Fx%29%2A14
5%2Bx=14%2FxMultiply all terms by x:
5x%2Bx%5E2=14Rearrange:
x%5E2%2B5x=14Solving by completing the square (adding (5/2)^2 to both sides):
x%5E2%2B5x%2B%285%2F2%29%5E2=14%2B%285%2F2%29%5E2
%28x%2B5%2F2%29%5E2=81%2F4
x%2B5%2F2=+0+%2B-sqrt%2881%2F4%29(Ignore the 0, just makes the equation editor work)
x%2B5%2F2=+0+%2B-+9%2F2 (Again, ignore the 0)
x=-5%2F2%2B-+9%2F2
x=%28-5%2B-+9%29%2F2
So x = %28-5%2B9%29%2F2=2 or %28-5-9%29%2F2=-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.