Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 504: 85

$x=-3$

Dividing both sides by 2 and using the concepts of radicals, the given equation, $ 2x^3=-54 ,$ is \begin{array}{l}\require{cancel} x^3=\dfrac{-54}{2} \\\\ x^3=-27 \\\\ x=\sqrt[3]{-27} \\\\ x=\sqrt[3]{(-3)^3} \\\\ x=-3 .\end{array}