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8 November, 02:54

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

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  1. 8 November, 05:02
    0
    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
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