# The sum of half a number and its reciprocal is the same as 51 divided by the number. How do you find the number?

##### 1 Answer

Jan 25, 2016

Write an equation to represent the situation

#### Explanation:

Place on a common denominator:

Now you can eliminate the denominators and solve the resulting quadratic equation.

Solve by factoring as a difference of squares.

(x + 10)(x - 10) = 0

x = -10 and 10

The numbers are -10 and 10.

**Exercises:**

- A third of a number added to four times the number's reciprocal is equal to half the quotient of 104 and the number.