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<x²-14

-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<x<7, x+2 will be positive, but x-7 will be negative, the the product of the two will be negative, then this is not a solution

So the solution for x is

x>7 or x<-2

hdjd

step-by-step explanation: