Answer:
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