Solve for x: x² - 9 = 0.

To solve the equation ( x^2 - 9 = 0 ), we start by rearranging it. The equation can be rewritten as ( x^2 = 9 ). To isolate ( x ), we take the square root of both sides. This gives us two possible solutions:

1. ( x = 3 )

2. ( x = -3 )

These solutions indicate that both positive and negative values of ( x ) satisfy the original equation since squaring either will yield 9, thus satisfying the condition that the square minus 9 equals zero.

Therefore, the solution set is expressed as ( x = 3 ) or ( x = -3 ), comprehensively represented by the choice indicating both solutions. This highlights the importance of recognizing that when solving quadratic equations, multiple solutions may exist, particularly when dealing with square roots.