To solve the equation x^3 - 1 = 0, you can find the cubic root of 1. The cubic root of 1 is 1, because 1^3 = 1. However, since x^3 - 1 = (x - 1)(x^2 + x + 1), you can also find the other two solutions of the equation by setting the second factor equal to zero: x^2 + x + 1 = 0 This quadratic equation does not have real solutions, because its discriminant is negative: b^2 - 4ac = (1)^2 - 4 * 1 * 1 = -3 < 0 Therefore, the only real solution of the equation x^3 - 1 = 0 is x = 1. If you want to find the complex solutions, you can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a = (-1 ± sqrt(-3)) / 2 So, the complex solutions are: x = (-1 + sqrt(-3)) / 2 and x = (-1 - sqrt(-3)) / 2 Or, using trigonometric form: x = cos(2π/3) + i * sin(2π/3) and x = cos(4π/3) + i * sin(4π/3) In summary, the solutions of the equation x^3 - 1 = 0 are: x = 1 (real solution) x = (-1 + sqrt(-3)) / 2 (complex solution) x = (-1 - sqrt(-3)) / 2 (complex solution)