Solve the binomial equation x^3 + 8 = 0 Solution To solve the binomial equation, we\'ll apply the formula of the sum of cubes: a^3 + b^3 = (a+b)(a^2 - ab + b^2) a^3 = x^3 a = x b^3 = 2^3 = 8 b = 2 x^3 + 8 = (x+2)(x^2 - 2x + 4) If x^3 + 8 = 0, then (x+2)(x^2 - 2x + 4) = 0 If a product is zero, then each factor could be zero. x + 2 = 0 We\'ll subtract 2 both sides: x1 = -2 x^2 - 2x + 4 = 0 We\'ll apply the quadratic formula: x2 = [2 + sqrt(4-16)]/2 x2 = (2+2isqrt3)/2 We\'ll factorize by 2: x2 = 2(1+isqrt3)/2 x2 = 1+isqrt3 x3 = 1- isqrt3 The roots of the equation are: {-2 , 1+isqrt3, 1- isqrt3 }..