Answer
$x = \frac{1}{2}$
Work Step by Step
$arccos~x+2~arcsin~\frac{\sqrt{3}}{2} = \pi$
$arccos~x+2~(\frac{\pi}{3}) = \pi$
$arccos~x = \frac{\pi}{3}$
$x = cos~\frac{\pi}{3}$
$x = \frac{1}{2}$
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