Solve using quadratic formulas

Question

x3+x-3x2-3=0

Answer 1

x^3 + x - 3x^2 - 3 = 0
(x^3 + x) - (3x^2 + 3) = 0
x(x^2 + 1) - 3(x^2 + 1) = 0
(x - 3)(x^2 + 1) = 0
x - 3 = 0 or x^2 + 1 = 0
x = 3 or x^2 + 1 = 0

If you use the quadratic formula on x^2 + 1 = 0, you will have:
x = [0 +/- sqrt(0^2 - 4(1)(1))] / [2(1)]
x = [+/- sqrt(-4)] / 2
x = sqrt(4)sqrt(-1) / 2 or x = -sqrt(4)sqrt(-1) / 2
x = 2i / 2 or x = -2i / 2
x = i or x = -i

It is more straight forward to use direct calculations though:
x^2 + 1 = 0
x^2 = -1
x = +/-sqrt(-1)
x = +/- i
x = i or x = -i

Hence, the final answer is x = 3 or x = i or x = -i