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

Step-by-step explanation:

Let the number be x

5 times the number is = 5*x=5x

Square do the number is x²

14 less than square the number is x²-14

So, given that

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

Therefore

5x
-x²+5x+14<0

Divide through by - 1, note, it will change the inequalities sign

x²-5x-14>0

Using factorization

x²+2x-7x-14>0

x (x+2) - 7 (x+2) >0

(x+2) (x-7) >0

So it is either x+2>0

x>-2

Or

x-7>0

x>7

Now, the range where x is correct

Note if x>-2 can't be true because x+2 will always be positive but x-7 can be positive or negative,

So let consider

x<-2, both x+2 and x-7 will be negative and the multiplication of the two will be positive, then, x<-2 is possible answer

Let look at x>7, Also, both x+2 and x-7 will be positive and the multiplication of the two will be positive, then, x>7 is possible answer.

So between - 2 and 7,

-2
So the solution for x is

x>7 or x<-2