Нуждаюсь в помощи! x+4>2√4-2x^2 4-2x^2 - это подкоренное выражение

Решите задачу:

$x+4\ \textgreater \ 2\sqrt{4-2x^2}, \\ \left\{\begin{array}{c} x+4\ \textgreater \ 0,\\4-2x^2 \geq0,\\(x+4)^2\ \textgreater \ 4(4-2x^2);\end{array}\right. \left\{\begin{array}{c} x\ \textgreater \ -4,\\x^2-2\leq0,\\9x^2-8x\ \textgreater \ 0;\end{array}\right. \left\{\begin{array}{c} x\ \textgreater \ -4,\\(x+\sqrt{2})(x-\sqrt{2})\leq0,\\x(x-\frac{8}{9})\ \textgreater \ 0;\end{array}\right. \\ \left\{\begin{array}{c} x\ \textgreater \ -4,\\-\sqrt{2}\leq x\leq\sqrt{2},\\ \left [ {{x\ \textless \ 0,} \atop {x\ \textgreater \ \frac{8}{9};}} \right. \end{array}\right. \left [ {{-\sqrt{2}\leq x\ \textless \ 0,} \atop {\frac{8}{9}\ \textless \ x\leq\sqrt{2};}} \right. \\$
$x\in[-\sqrt{2};0)\cup(\frac{8}{9};\sqrt{2}]$