# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.4 De Moivre's Theorem: Powers and Roots of Complex Numbers - 8.4 Exercises - Page 383: 50

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.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.