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

Jun 19, 2016

The number is either 5 or $- \frac{2}{5}$

#### Explanation:

Let x be the number.

We are told that the number subtracted from twice its reciprocal is equal to $- \frac{23}{5}$

Hence: $\frac{2}{x} - x = - \frac{23}{5}$

Multiply through by x and cross multiply $\to 5 \left(2 - {x}^{2}\right) = - 23 x$

Expand $\to 10 - 5 {x}^{2} = - 23 x$

$- 5 {x}^{2} + 23 x + 10 = 0$

$5 {x}^{2} - 23 x - 10 = 0$

Factorise $\to \left(x - 5\right) \left(5 x + 2\right) = 0$

Hence x = either 5 or $- \frac{2}{5}$