Remove parentheses.
\[\frac{2}{3}x\times \frac{9}{8}x=\frac{27}{64}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{2x\times 9x}{3\times 8}=\frac{27}{64}\]
Take out the constants.
\[\frac{(2\times 9)xx}{3\times 8}=\frac{27}{64}\]
Simplify \(2\times 9\) to \(18\).
\[\frac{18xx}{3\times 8}=\frac{27}{64}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{18{x}^{2}}{3\times 8}=\frac{27}{64}\]
Simplify \(3\times 8\) to \(24\).
\[\frac{18{x}^{2}}{24}=\frac{27}{64}\]
Simplify \(\frac{18{x}^{2}}{24}\) to \(\frac{3{x}^{2}}{4}\).
\[\frac{3{x}^{2}}{4}=\frac{27}{64}\]
Multiply both sides by \(4\).
\[3{x}^{2}=\frac{27}{64}\times 4\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[3{x}^{2}=\frac{27\times 4}{64}\]
Simplify \(27\times 4\) to \(108\).
\[3{x}^{2}=\frac{108}{64}\]
Simplify \(\frac{108}{64}\) to \(\frac{27}{16}\).
\[3{x}^{2}=\frac{27}{16}\]
Divide both sides by \(3\).
\[{x}^{2}=\frac{\frac{27}{16}}{3}\]
Simplify \(\frac{\frac{27}{16}}{3}\) to \(\frac{27}{16\times 3}\).
\[{x}^{2}=\frac{27}{16\times 3}\]
Simplify \(16\times 3\) to \(48\).
\[{x}^{2}=\frac{27}{48}\]
Simplify \(\frac{27}{48}\) to \(\frac{9}{16}\).
\[{x}^{2}=\frac{9}{16}\]
Take the square root of both sides.
\[x=\pm \sqrt{\frac{9}{16}}\]
Simplify \(\sqrt{\frac{9}{16}}\) to \(\frac{\sqrt{9}}{\sqrt{16}}\).
\[x=\pm \frac{\sqrt{9}}{\sqrt{16}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[x=\pm \frac{3}{\sqrt{16}}\]
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[x=\pm \frac{3}{4}\]
Decimal Form: ±0.75
x=3/4,-3/4
