This document provides the steps to solve the equation x^4-7x^2-8=0. It first factors the equation into (x^2 -8)(x^2 + 1) = 0, then further factors each term to get (x- sqrt8)(x+sqrt8)(x+ i) (x-i)= 0. This reveals there are 4 roots: x1= sqrt8 = 2sqrt2, x2= - 2sqrt2, x3= i, x4= -i. Therefore, the solutions for x are -2sqrt2, 2sqrt3, i, -i.