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

Question

asked Aug 23, 2021 180k views

1 Answer

Kyle Robson · Answer 1 · 2021-08-27T13:50:55+0000

Answer:

The negative solution is

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

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

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