# 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

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 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(16877)   (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(7569)   (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