Solve the equation $-7 x^{2}-8+x^{4}=0$. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE. \[ x= \] help (numbers)

Step 1 ：We can rearrange the equation $-7 x^{2}-8+x^{4}=0$ to the form $x^4-7x^2-8=0$.

Step 2 ：This equation is a quadratic equation in terms of $x^2$. We can solve it by factoring: $(x^2-8)(x^2+1)=0$.

Step 3 ：Setting each factor equal to zero gives us $x^2-8=0$ and $x^2+1=0$.

Step 4 ：Solving $x^2-8=0$ gives $x^2=8$, so $x=\pm\sqrt{8}=\pm2\sqrt{2}$.

Step 5 ：Solving $x^2+1=0$ gives $x^2=-1$, so $x=\pm i$.

Step 6 ：Therefore, the solutions of the original equation are $x=\boxed{2\sqrt{2},-2\sqrt{2},i,-i}$.