SOLUTION: if a number is subtracted from twice its reciprocal the result is -23/5. what is the number?

Question 629591: if a number is subtracted from twice its reciprocal the result is -23/5. what is the number?
Found 2 solutions by stanbon, 55305:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if a number is subtracted from twice its reciprocal the result is -23/5. what is the number?
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Let the number be "x":
2(1/x) - x = -23/5
Multiply thru by 5x to get:
10 - 5x^2 = -23x
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Rearrange:
5x^2 -23x - 10 = 0
Factor:
5x^2-25x+2x-10 = 0
5x(x-5)+2(x-5) = 0
(x-5)(5x+2) = 0
The number is 5 or -2/5
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Cheers,
Stan H.

Answer by 55305(86) (Show Source): You can put this solution on YOUR website!
First we should write an algebraic equation. So pretend the number is x. So twice the reciprocal is 2/x and if we subtract the number from that to get 2/x-x. Then we set that equal to -23/5 and solve.
2/x-x=-23/5
Multiply both sides by 5x to get rid of the fractions: 10-5x^2=-23x
Convert it to the ax^2+bx+c=0: -5x^2+23x+10=0

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: x=-0.4,x=5.

Graphical form: Equation was fully solved.
Text form: -5x^2+23x+10=0 simplifies to 0=0
Cartoon (animation) form:
For tutors: simplify_cartoon( -5x^2+23x+10=0 )

If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Equation is a quadratic equation: -5*x^2+23*x+10 =0, and has solutions -0.4,5
It becomes .
Result:
This is an equation! Solutions: x=-0.4,x=5.

Universal Simplifier and Solver

Done!

The two answers you get are -0.4, and 5, so lets check which one is right.
if x= -2/5: -10/2-(-2/5)= -5+2/5= -23/5 and so that is the answer.
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