What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

To get the solutions to the equation x^6 + 6x^3 + 5 = 0 using factoring. Expanding x^6 + 6x^3 + 5 = 0 gives x^6 + x^3 + 5x^3 + 5 = 0, Factoring x^6 + x^3 + 5x^3 + 5 = 0 gives x^3 (x^3 + 1) + 5 (x^3 + 1) = 0, Grouping x^3 (x^3 + 1) + 5 (x^3 + 1) = 0 gives (x^3 + 5) (x^3 + 1) = 0 Solving (x^3 + 5) (x^3 + 1) = 0 gives x^3 + 5 = 0 or x^3 + 1 = 0 x^3 = - 5 or x^3 = - 1 x = cube root of - 5 or x = cube root of - 1 x = - 1.71 or x = - 1