Question 216499
A natural number decreased by 30 times it's reciprocal is 1.
Find the number.
:
x = the number
:
The problem
x - 30({{{1/x}}}) = 1 
x - {{{30/x}}} = 1
Multiply equation by x, results:
x^2 - 30 = x
Arrange as a quadratic equation
x^2 - x - 30 = 0
Factor
(x-6)(x+5) = 0
Two solutions
x = 6
x = -5
:
Check x=6 in original equation
6 - 30({{{1/6}}}) = 1
6 - 5 = 1
;
Check x=-5
-5 - 30({{{1/(-5)}}}) = 1 
-5 + 6 = 1
:
Not that hard, right?