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

(x-9) ²=-3+x

expand

x²-18x+81=-3+x

minus x both sides and add 3

x²-19x+84=0

factor

what 2 numbers multiply to get 84 and add to get - 19?

-7 and - 12

(x-7) (x-12) = 0

set equal to 0

x-7=0

x=7

x-12=0

x=12

the number is 7 or 12

both work