Answer
$x=\left\{ -3\sqrt{3},3\sqrt{3} \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
27-x^2=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
-x^2=-27
\\\\
x^2=27
.\end{array}
Taking the square root of both sides, the solutions to the equation above are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{27}
\\\\
x=\pm\sqrt{9\cdot3}
\\\\
x=\pm\sqrt{(3)^2\cdot3}
\\\\
x=\pm3\sqrt{3}
.\end{array}
Hence, the solution is $
x=\left\{ -3\sqrt{3},3\sqrt{3} \right\}
.$
