Question

$$9 { x }^{ 2 } =4$$

Answer

x=2/3,-2/3

Solution


Divide both sides by \(9\).
\[{x}^{2}=\frac{4}{9}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{4}{9}}\]
Simplify  \(\sqrt{\frac{4}{9}}\)  to  \(\frac{\sqrt{4}}{\sqrt{9}}\).
\[x=\pm \frac{\sqrt{4}}{\sqrt{9}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[x=\pm \frac{2}{\sqrt{9}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[x=\pm \frac{2}{3}\]

Decimal Form: ±0.666667