1. **Problem:** Solve the quadratic equation $x^2 - 4 = 0$ (pure quadratic). 2. **Formula and rules:** A pure quadratic equation has the form $ax^2 + c = 0$. To solve, isolate $x^2$ and take the square root of both sides: $$x^2 = -\frac{c}{a}$$ Then, $$x = \pm \sqrt{-\frac{c}{a}}$$ Remember, if the value under the square root is negative, solutions are complex. 3. **Work:** Given $x^2 - 4 = 0$, rewrite as: $$x^2 = 4$$ Take the square root: $$x = \pm \sqrt{4}$$ $$x = \pm 2$$ 4. **Answer:** The solutions are $x = 2$ and $x = -2$.