Answer:
The negative solution is
[tex] - 2[/tex]
Step-by-step explanation:
Let the number be
Then 5 times the number is 5x.
14 less than the square of the number is
[tex] {x}^{2} - 14[/tex]
So our equation becomes
[tex]5x = {x}^{2}- 14[/tex]
This implies that
[tex]{x}^{2} - 5x - 14 = 0[/tex]
We factor to get:
[tex] {x}^{2} - 7x + 2x - 14 = 0[/tex]
[tex]x(x - 7) + 2(x - 7) = 0[/tex]
[tex](x - 7)(x + 2) = 0[/tex]
[tex]x + 7 = 0 \: or \: x - 2 = 0[/tex]
[tex]x = 7 \: or \: x = - 2[/tex]
