Chapter 5 - Polynomials and Polynomial Functions - 5-5 Theorems About Roots of Polynomial Equations - Practice and Problem-Solving Exercises - Page 317: 60

$x = \pm \space 12i$

Divide both sides of the equation by $2$: $\dfrac{2x^2+288}{2}=\dfrac{0}{2}\\ x^2 + 144 = 0$ $x^2 = -144$ Take the square root of both sides: $x = \pm\sqrt{-144}\\ x = \pm\sqrt {(-1)(144)}$ The square root of $-1$ is $i$, and the square root of $144$ is $12$: $x = \pm \space12i$