[tex]\huge\text{$x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4}$}[/tex]
To solve for [tex]x[/tex], we need to isolate it on one side of the equation.
Take the square root of both sides, making sure to use both positive and negative roots.
[tex]\begin{aligned}(x-4)^2&=33\\x-4&=\pm\sqrt{33}\end{aligned}[/tex]
[tex]\sqrt{33}[/tex] cannot be simplified, so we'll leave it as-is.
Add [tex]4[/tex] to both sides to fully isolate [tex]x[/tex].
[tex]x=\pm\sqrt{33}+4[/tex]
Expand the solution by making two solutions, one where [tex]\sqrt{33}[/tex] is positive and one where it's negative.
[tex]x=\sqrt{33}+4,\ x=-\sqrt{33}+4\\x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4}[/tex]
