Regroup terms.
\[10x\sqrt{3{x}^{2}+}+8\sqrt{3}=0\]
Separate terms with roots from terms without roots.
\[10x\sqrt{3{x}^{2}+}=-8\sqrt{3}\]
Square both sides.
\[300{x}^{4}=192\]
Divide both sides by \(300\).
\[{x}^{4}=\frac{192}{300}\]
Simplify \(\frac{192}{300}\) to \(\frac{16}{25}\).
\[{x}^{4}=\frac{16}{25}\]
Take the \(4\)th root of both sides.
\[x=\pm \sqrt[4]{\frac{16}{25}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[x=\pm \frac{\sqrt[4]{16}}{\sqrt[4]{25}}\]
Calculate.
\[x=\pm \frac{2}{\sqrt[4]{25}}\]
Rewrite \(25\) as \({5}^{2}\).
\[x=\pm \frac{2}{\sqrt[4]{{5}^{2}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[x=\pm \frac{2}{{5}^{\frac{2}{4}}}\]
Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
\[x=\pm \frac{2}{{5}^{\frac{1}{2}}}\]
Convert \({5}^{\frac{1}{2}}\) to square root.
\[x=\pm \frac{2}{\sqrt{5}}\]
Decimal Form: ±0.894427
x=2/sqrt(5),-2/sqrt(5)
