Algebraic Manipulation !

Geometry Level 5

Let \(x\in \mathbb{R}^{ + }\) and \(f\left( x \right) = \sqrt { 576+{ x }^{ 2 }-24x } +\sqrt { 49+{ x }^{ 2 }-7\sqrt { 3 } x } \).

If we set \(x\) positive variable in such a way that \(f\left( x \right) \) is Minimum possible, then for this condition, find the value of \[E\quad =\quad \frac { 336-24\sqrt { 3 } x -7x }{ 4 } .\]

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