The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution

n = -3

Step-by-step explanation:

The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.

I'm going to call the number "n."

n² - 24 =  5n      subtract 5n from both sides to get the equation equal to zero

- 5n        -5n

n² - 5n - 24 = 0   factor the trinomial into the multiplicatin of two binomials

                           we need factors (numbers that multiply) to -24 that add up to

                           -5.  The only factors for -24 that will add up to -5 are -8 and 3.

(n-8)(n+3) = 0     set each binomial equal to zero and solve for n

n-8  =  0     or    n+3  =  0

 +8    +8               -3     -3

 n   =  8     or        n  = -3       n = -3 is the negative solution

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