Question

$${ x }^{ 2 } - \frac{ 49 }{ 64 } =0$$

Answer

x=7/8,-7/8

Solution


Add \(\frac{49}{64}\) to both sides.
\[{x}^{2}=\frac{49}{64}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{49}{64}}\]
Simplify  \(\sqrt{\frac{49}{64}}\)  to  \(\frac{\sqrt{49}}{\sqrt{64}}\).
\[x=\pm \frac{\sqrt{49}}{\sqrt{64}}\]
Since \(7\times 7=49\), the square root of \(49\) is \(7\).
\[x=\pm \frac{7}{\sqrt{64}}\]
Since \(8\times 8=64\), the square root of \(64\) is \(8\).
\[x=\pm \frac{7}{8}\]

Decimal Form: ±0.875