SOLUTION: Twice a certain natural number exceeds eight times its reciprocal by fifteen. What is the number? I know that a number can be represented by x and twice that number is 2x but I

Question 340205: Twice a certain natural number exceeds eight times its reciprocal by fifteen. What is the number?
I know that a number can be represented by x and twice that number is 2x but I do not know how to represent a reciprocal in a word equation.
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Multiply both sides by , collect terms on the left, and factor:

Finish solving for , and then discard the negative root (you are looking for a natural number if you remember)

John

My calculator said it, I believe it, that settles it

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let the number be x.
2x=8/x + 15
2x^2=8+15x Multiply each side by x.
2x^2-15x-8=0
2x^2+x-16x-8=0
x(2x+1)-8(2x+1)=0
(x-8)(2x+1)=0
x=8
.
Ed
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