\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{32-8x^2}+4=x+4\\\sqrt{32-8x^2}+4=-x-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{32-8x^2}=x\\\sqrt{32-8x^2}=-x-8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>=0\\32-8x^2=x^2\end{matrix}\right.\\\left\{{}\begin{matrix}x< =-8\\32-8x^2=x^2+16x+64\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>=0\\32-9x^2=0\end{matrix}\right.\\\left\{{}\begin{matrix}x< =-8\\-9x^2-16x-32=0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=0\\9x^2=32\end{matrix}\right.\)
=>\(x=\sqrt{\dfrac{32}{9}}=\dfrac{4\sqrt{2}}{3}\)
