Question 427846
Let {{{z = x^2}}} so our quartic equation becomes {{{4z^2 - 2z - 4 = 2}}} --> {{{4z^2 - 2z - 6 = 0}}} --> {{{2z^2 - z - 3 = 0}}}. This factors to {{{(2z - 3)(z + 1) = 0}}}, so either {{{z = 3/2}}} or {{{z = -1}}}. Substituting back into our expression for z in terms of x, we obtain

{{{x^2 = 3/2}}} --> {{{x = sqrt(3/2)}}}, {{{x = -sqrt(3/2)}}}

{{{x^2 = -1}}} --> {{{x = i}}}, {{{x = -i}}} (i is the imaginary unit, equal to {{{sqrt(-1)}}}.