SOLUTION: The sum of a number and four times its reciprocal is 29/5.Find the number

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Question 427792: The sum of a number and four times its reciprocal is 29/5.Find the number
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of a number and four times its reciprocal is 29/5.Find the number
Let's call the number n.
The reciprocal would be 1%2Fn
So the formula should look like.
n%2B4%2A%281%2Fn%29=29%2F5
now multiply every term on both sides by n, the 1%2Fn in the 4%2A%281%2Fn%29 will cancel to become 1, leaving you with 4*1=4
n%5E2%2B4=%2829%2F5%29%2An multiply both sides by 5.
5n%5E2%2B20=29n subtract 29n from both sides
5n%5E2-29n%2B20=0 now you have a solvable quadratic equation, that factors into.
%285n-4%29%28n-5%29=0
So n=5 or 5n-4=0 -> 5n=4 divide both sides by 5 n=5%2F4