Question

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

Answer 1

(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