Answer
The three solutions for the value of $x$ are:
$x = -3$
$x = \frac{3 + 3\sqrt{3}~i}{2}$
$x = \frac{3 - 3\sqrt{3}~i}{2}$
Work Step by Step
$x^3+27=0$
$(x+3)(x^2-3x+9) = 0$
If $(x+3) = 0$, then $x = -3$
We can use the quadratic formula to find the solutions when $(x^2-3x+9) = 0$:
$x = \frac{3 \pm \sqrt{(-3)^2-(4)(1)(9)}}{(2)(1)}$
$x = \frac{3 \pm \sqrt{-27}}{2}$
$x = \frac{3 \pm 3\sqrt{3}~i}{2}$
The three solutions for the value of $x$ are:
$x = -3$
$x = \frac{3 + 3\sqrt{3}~i}{2}$
$x = \frac{3 - 3\sqrt{3}~i}{2}$
These three solutions are equivalent to the three solutions found in Exercise 36.
