Question

$$16 { x }^{ 2 } =81$$

Answer

x=9/4,-9/4

Solution


Divide both sides by \(16\).
\[{x}^{2}=\frac{81}{16}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{81}{16}}\]
Simplify  \(\sqrt{\frac{81}{16}}\)  to  \(\frac{\sqrt{81}}{\sqrt{16}}\).
\[x=\pm \frac{\sqrt{81}}{\sqrt{16}}\]
Since \(9\times 9=81\), the square root of \(81\) is \(9\).
\[x=\pm \frac{9}{\sqrt{16}}\]
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[x=\pm \frac{9}{4}\]

Decimal Form: ±2.25