Answer
$x=\pm \frac{\sqrt{2}}{3}$
Work Step by Step
$9{{x}^{2}}-2=0$
Add $2$ on both sides:
$\begin{align}
& 9{{x}^{2}}-2+2=2 \\
& 9{{x}^{2}}=2
\end{align}$
Now, divide by 9 on both sides:
$\begin{align}
& 9{{x}^{2}}=2 \\
& \frac{9{{x}^{2}}}{9}=\frac{2}{9} \\
\end{align}$
Combine the like terms:
$\begin{align}
& \frac{9{{x}^{2}}}{9}=\frac{2}{9} \\
& {{x}^{2}}=\frac{2}{9}
\end{align}$
Now, making the square root on both sides:
$\begin{align}
& {{x}^{2}}=\frac{2}{9} \\
& \sqrt{{{x}^{2}}}=\sqrt{\frac{2}{9}}
\end{align}$
Now, from the principle of square property,
$x=\frac{\sqrt{2}}{3}\text{ or }-\frac{\sqrt{2}}{3}$
Therefore, the value of $x$ from the provided expression $9{{x}^{2}}-2=0$ is $x=\pm \frac{\sqrt{2}}{3}$
