Using the quadratic formula: \( t = \frac{4 \pm \sqrt{16 + 4}}{2} = \frac{4 \pm \sqrt{20}}{2} = \frac{4 \pm 2\sqrt{5}}{2} = 2 \pm \sqrt{5} \).

["Using the Quadratic Formula: Solve Quadratic Equations with Ease", "Solving quadratic equations is a fundamental skill in algebra, and the quadratic formula offers a reliable method for finding solutions when factoring is difficult or impossible. One classic example demonstrates how this powerful tool simplifies radical expressions to reveal the roots clearly.", "Consider the quadratic equation:", "[\nt = \frac{4 \pm \sqrt{16 + 4}}{2}\n]", "### Step-by-Step Derivation", "Start with the discriminant under the square root:", "[\n\sqrt{16 + 4} = \sqrt{20}\n]", "Simplify the square root:", "[\n\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}\n]", "Substitute back into the formula:", "[\nt = \frac{4 \pm 2\sqrt{5}}{2}\n]", "Split into two solutions using the ± operator:", "[\nt = \frac{4 + 2\sqrt{5}}{2} \quad \ ext{or} \quad t = \frac{4 - 2\sqrt{5}}{2}\n]", "Simplify each expression:", "[\nt = 2 + \sqrt{5} \quad \ ext{and} \quad t = 2 - \sqrt{5}\n]", "Thus, the solutions are:", "[\nt = 2 \pm \sqrt{5}\n]", "### Why This Matters", "Using the quadratic formula eliminates guesswork and simplifies radical expressions systematically. This particular equation—though straightforward—illustrates how simplifying square roots improves clarity and accuracy when solving quadratic equations. From physics to engineering, mastering this formula enables efficient problem-solving with real-world applications.", "### Practice Makes Perfect", "Once comfortable with basic simplifications, try problems involving more complex discriminants. With practice, solving quadratic equations using the quadratic formula becomes second nature, empowering you to tackle advanced mathematics confidently.", "---", "Looking for more masterclasses in algebra? Explore our guides on factoring quadratics, completing the square, and more – perfect for students and math enthusiasts alike!"]