Chapter 5 - Polynomials and Polynomial Functions - 5-5 Theorems About Roots of Polynomial Equations - Practice and Problem-Solving Exercises - Page 317: 59

$x = ± 9i$

Subtract $81$ from both sides to shift the constant to the right side of the equation: $x^2+81-81=0-81\\ x^2 = -81$ Take the square root of both sides: $x = \pm\sqrt {-81}\\ x = \pm\sqrt {(-1)(81)}$ The square root of $-1$ is $± i$, and the square root of $81$ is $± 9$: $x = ± 9i$