Answer:
[tex]x=5, \\x=-1[/tex]
Step-by-step explanation:
Given [tex](x-2)^2=9[/tex], to solve for [tex]x[/tex], our goal is to isolate [tex]x[/tex].
Take the square root of both sides:
[tex]x-2=\pm\sqrt{9},\\x-2=\pm 3[/tex](recall that [tex]3^2=(-3)^2=9[/tex]).
Therefore, we have two cases:
[tex]\begin{cases}x-2=3,x=\boxed{5} \\x-2=-3, x=\boxed{-1}\end{cases}[/tex]
