\[x^{4} + 6x^{2} - 27 = 0\]
\[Пусть\ x^{2} = t \geq 0:\]
\[t^{2} + 6t - 27 = 0\]
\[t_{1} + t_{2} = - 6;\ \ \ t_{1} \cdot t_{2} = - 27\]
\[t_{1} = - 9\ (не\ подходит);\ \ t_{2} = 3.\]
\[x^{2} = 3\]
\[x = \pm \sqrt{3}.\]
\[Ответ:x = \pm \sqrt{3}.\]