Question

$$49 { x }^{ 2 } -4=0$$

Answer

x=2/7,-2/7

Solution


Add \(4\) to both sides.
\[49{x}^{2}=4\]
Divide both sides by \(49\).
\[{x}^{2}=\frac{4}{49}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{4}{49}}\]
Simplify  \(\sqrt{\frac{4}{49}}\)  to  \(\frac{\sqrt{4}}{\sqrt{49}}\).
\[x=\pm \frac{\sqrt{4}}{\sqrt{49}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[x=\pm \frac{2}{\sqrt{49}}\]
Since \(7\times 7=49\), the square root of \(49\) is \(7\).
\[x=\pm \frac{2}{7}\]

Decimal Form: ±0.285714