SOLUTION: The sum of a number and 25 times its reciprocal is 10. Find the number.

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Question 140140: The sum of a number and 25 times its reciprocal is 10. Find the number.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the number
then 1/x is the reciprocal
25 times the reciprocal is:
25/x
Now we are told that x+(25/x)=10 multiply each term by x
x^2+25=10x subtract 10x from each side
x^2-10x+25=10x-10x or
x^2-10x+25=0----quadratic in standard form and it can be factored
(x-5)^2=0 take sqrt of both sides
x-5=0
x=5
CK
5+25/5=10
10=10
Hope this helps---ptaylor