Question

5 times a number is 14 less than the square of that number. Find the negative solution.

Answer 1

The negative solution is

`- 2`

Explanation:

Let the number be

Then 5 times the number is 5x.

14 less than the square of the number is

`{x}^(2) - 14`

So our equation becomes

`5x = {x}^(2)- 14`

This implies that

`{x}^(2) - 5x - 14 = 0`

We factor to get:

`{x}^(2) - 7x + 2x - 14 = 0`

`x(x - 7) + 2(x - 7) = 0`

`(x - 7)(x + 2) = 0`

`x + 7 = 0 \: or \: x - 2 = 0`

`x = 7 \: or \: x = - 2`