x^2-6x+9=color(white)a8
color(white)(aaaa^2aa)-9color(white)a-9color(white)(aaa)Subtract 9 from both sides
x^2-color(red)(6)xcolor(white)(aaa)=-1
Divide the coefficient of the x term color(red)(6) by 2 and square the result.
color(red)6/2=color(limegreen)3 => color(limegreen)3^2=color(blue)9
Add color(blue)9 to both sides.
x^2-6x+color(blue)9=-1+color(blue)9
x^2-6x+9=8
Note that you got the exact equation you started with! The next step is to factor the left side into the square of a binomial. The left side of this equation started out in factorable form, but I demonstrated all the steps anyway for future reference.
Factor the left side
(x-3)(x-3)=8color(white)(aaa)
#Rewrite as the square of a binomial.
(x-color(limegreen)3)^2=8color(white)(aaa)Note that color(limegreen)3 is the number you got when you divided the coefficient of the x term by 2.
Square root both side.
sqrt((x-3)^2) =sqrt8
x-3=sqrt(4*2)
x-3= +-2sqrt2
color(white)a+3color(white)(aaaaaaaa)+3
x=3+-2sqrt2