Answer
$9\text{ and 3}$.
Work Step by Step
${{x}^{2}}-12x+36=9$
Rewrite the expression ${{x}^{2}}-12x+36=9$:
$\begin{align}
& {{x}^{2}}-12x+36=9 \\
& {{\left( x-6 \right)}^{2}}=9
\end{align}$
Now, taking the square root on both sides:
$\begin{align}
& {{\left( x-6 \right)}^{2}}=9 \\
& \sqrt{x-{{6}^{2}}}=\sqrt{9}
\end{align}$
Now, from the principle of squares property,
$x-6=3$ or $x-6=-3$
Consider the term, $x-6=3$
Add 6 to both sides:
$\begin{align}
& x-6+6=3+6 \\
& x=9
\end{align}$
Consider the term, $x-6=-3$
Add 6 to both sides:
$\begin{align}
& x-6+6=-3+6 \\
& x=3
\end{align}$
Therefore, the value of $x$ from the provided expression ${{x}^{2}}-12x+36=9$ are $9\text{ and 3}$.
