The square of 9 less than a number is 3 less than the number. What is the number?

-12 or 7

-12 or - 7

1-7 or 12

7 or 12

7, 12

Step-by-step explanation:

(n-9) ^2 = n-3

Foil the right

n^2 - 18n + 81 = n-3

Subtract n from each side

n^2 - 19n + 81 = -3

Add 3 to each side

n^2 - 19n + 84 = 0

Factor

What 2 numbers multiply to 84 and add to - 19

-12*-7 = 84

-12+-7 = - 19

(n-7) (n-12) = 0

Using the zero product property

n-7 = 0 n-12 = 0

n=7 n=12