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?
---
Let the number be "x":
2(1/x) - x = -23/5
Multiply thru by 5x to get:
10 - 5x^2 = -23x
---
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
===============================
Cheers,
Stan H.
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
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.
(
