Solve x² - 9 = 0

Step-by-step solution

1. Recognise $x^2 - 9$ as a difference of squares $a^2 - b^2$ with $a = x$ and $b = 3$.

2. Apply the identity $a^2 - b^2 = (a-b)(a+b)$: $(x - 3)(x + 3) = 0$.

3. Set each factor to zero: $x - 3 = 0$ or $x + 3 = 0$.

4. Solve: $x = 3$ or $x = -3$.