X cubed plus x equals -2?

Answer 1

x3 + x = -2 => x3 + x + 2 = 0 => x3 + x2 - x2 - x + 2x - 2 = 0 => x2(x+1) - x(x+1) + 2(x+1) = 0 => (x+1)*(x2-x+2) = 0 Setting the first bracket equal to zero gives the only real solution, which is x = -1 The second bracket gives the complex roots, x = ½*[1 +or- i*sqrt(7)]