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