If a number is subtracted from twice its reciprocal, the result is -23/5. What is the number?

Question

You can solve this by using a quadratic equation.

Answer 1

"You can solve this by using a quadratic equation" is a pretty big clue!

 

Let's see, can we put "If a number is subtracted from twice its reciprocal, the result is -23/5" into the form of an equation?

 

Let x be the number we want to find ("What is the number?"  So, the words translate to:

         2(1/x)  -  x  =  -23/5                    [for practice, PLZ match this to the words]

 

           10 - 5x²  = -23x               [multiply everything by 5x]

           5x² -23x -10 = 0                [rearrange and set to 0 to solve

                                               ('solve' means to find x that makes expression 0)]

 

The quadratic equation (look it up if you don't remember it] gives us two possibilities:

                  x = 5  and  x = -0.4

 

To check:

    Is  2(1/5) + 5 = -23/5   ?

        -2/5  +  25/5   =  -23/5     yes

 

    Is 2(1/(-0.4))  + (-0.4)  = -23/5   ?

           -5  +  (-0.4)   =  -4.6  ?    yes