Question

$${ x }^{ 2 } - \frac{ 1 }{ 484 } =0$$

Answer

x=1/22,-1/22

Solution


Add \(\frac{1}{484}\) to both sides.
\[{x}^{2}=\frac{1}{484}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{1}{484}}\]
Simplify  \(\sqrt{\frac{1}{484}}\)  to  \(\frac{\sqrt{1}}{\sqrt{484}}\).
\[x=\pm \frac{\sqrt{1}}{\sqrt{484}}\]
Simplify  \(\sqrt{1}\)  to  \(1\).
\[x=\pm \frac{1}{\sqrt{484}}\]
Since \(22\times 22=484\), the square root of \(484\) is \(22\).
\[x=\pm \frac{1}{22}\]

Decimal Form: ±0.045455