Use quadratic formula: \( t = \frac{4 \pm \sqrt{16 + 36}}{2} = \frac{4 \pm \sqrt{52}}{2} = \frac{4 \pm 2\sqrt{13}}{2} = 2 \pm \sqrt{13} \)

["### Solving Quadratic Equations with the Quadratic Formula: A Step-by-Step Guide", "When solving quadratic equations, one of the most powerful tools in algebra is the quadratic formula. Whether you're a student tackling algebra 2 or a math enthusiast, understanding how to apply this formula can simplify complex problems involving parabolas, projectile motion, or vital rate calculations. In this article, we’ll break down one classic example using the quadratic formula:", "[\nt = \frac{4 \pm \sqrt{16 + 36}}{2} = \frac{4 \pm \sqrt{52}}{2} = \frac{4 \pm 2\sqrt{13}}{2} = 2 \pm \sqrt{13}\n]", "---", "#### What Is the Quadratic Formula?", "The standard quadratic equation is:", "[\nat^2 + bt + c = 0\n]", "The quadratic formula solves for ( t ) directly:", "[\nt = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Using this formula is especially helpful when factoring is difficult or impossible — common scenarios in advanced algebra and applied math.", "---", "#### Step-by-Step: Solving ( t = \frac{4 \pm \sqrt{16 + 36}}{2} )", "Let’s apply the formula step by step using the problem:", "[\nt = \frac{4 \pm \sqrt{16 + 36}}{2}\n]", "1. Compute the discriminant\n Inside the square root, calculate:\n [\n 16 + 36 = 52\n ]\n So the equation becomes:\n [\n t = \frac{4 \pm \sqrt{52}}{2}\n ]", "2. Simplify the square root\n Factor 52 as ( 4 \cdot 13 ), so:\n [\n \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}\n ]\n Substitute back:\n [\n t = \frac{4 \pm 2\sqrt{13}}{2}\n ]", "3. Factor and simplify numerator\n Factor a 2 in the numerator:\n [\n t = \frac{2(2 \pm \sqrt{13})}{2} = 2 \pm \sqrt{13}\n ]", "---", "#### Final Solution", "The two solutions are:", "[\nt = 2 + \sqrt{13} \quad \ ext{and} \quad t = 2 - \sqrt{13}\n]", "These represent two distinct values of ( t ) — useful in modeling real-world phenomena such as intersection times, optimal decisions in business, or time-based predictions in physics.", "---", "#### Why Use the Quadratic Formula?", "- Handles irrational numbers and complex numbers with ease.\n- Works for any quadratic equation without relying on factoring.\n- Essential for advanced math applications like calculus, engineering, and economics.", "Whether you're solving for time, distance, revenue, or height over time, mastering the quadratic formula puts you ahead in algebra and beyond.", "---", "#### Tips to Master the Quadratic Formula Quickly", "- Always simplify the discriminant fully before taking square roots.\n- Factor constants inside the square root whenever possible.\n- Write answers clearly in exact radical form when required.\n- Practice with varied coefficients to build fluency.", "---", "#### Conclusion", "Understanding how to apply the quadratic formula to expressions like:", "[\n\boxed{t = 2 \pm \sqrt{13}}\n]", "is fundamental for anyone studying algebra or pursuing STEM fields. This method transforms complex quadratic expressions into clear, actionable solutions. Keep practicing — and unlock more power in your math toolkit!", "---", "Keywords: quadratic formula, solve quadratic equation, discriminant, algebraic solutions, ( t = \frac{4 \pm \sqrt{16 + 36}}{2} ), simplify radical expressions, solve quadratic equations step by step, algebra tips, step-by-step quadratic solution, real-world applications of quadratics."]