Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 33

$x=-3$ or $x=3$

Using the definition of the absolute value, we have $$\displaystyle |x^2-9|=0\\ \Longrightarrow x^2-9=0\\ \Longrightarrow x^2=9 \\ \Longrightarrow x=\pm\sqrt 9\\ \Longrightarrow x=\pm3 $$ Thus, we have: $x=-3$ or $x=3$