Regroup terms.
\[11\sqrt{{x}^{2}+}-x=\sqrt{3}\]
Separate terms with roots from terms without roots.
\[11\sqrt{{x}^{2}+}=\sqrt{3}+x\]
Square both sides.
\[121{x}^{2}+=3+2\sqrt{3}x+{x}^{2}\]
Move all terms to one side.
\[121{x}^{2}-3-2\sqrt{3}x-{x}^{2}=0\]
Simplify \(121{x}^{2}-3-2\sqrt{3}x-{x}^{2}\) to \(120{x}^{2}-3-2\sqrt{3}x\).
\[120{x}^{2}-3-2\sqrt{3}x=0\]
Use the Quadratic Formula.
In general, given \(a{x}^{2}+bx+c=0\), there exists two solutions where:
\[x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}\]
In this case, \(a=120\), \(b=-2\sqrt{3}\) and \(c=-3\).
\[{x}^{}=\frac{2\sqrt{3}+\sqrt{{(-2\sqrt{3})}^{2}-4\times 120\times -3}}{2\times 120},\frac{2\sqrt{3}-\sqrt{{(-2\sqrt{3})}^{2}-4\times 120\times -3}}{2\times 120}\]
Simplify.
\[x=\pm \sqrt{3}\]
\[x=\pm \sqrt{3}\]
Decimal Form: ±1.732051
x=-sqrt(3),sqrt(3)
