Step-by-Step Solution & Personalized Explanation Step 1: Identify coefficients The general quadratic equation is �. Here: � � � Step 2: Check for factorization We try to factor �. We need two numbers that multiply to � and add to �. Numbers are -2 and -3. Step 3: Split the middle term Step 4: Factor by grouping Step 5: Factor out common term Step 6: Solve for x ✅ Solution: � or � Alternative Method: Quadratic Formula  Common Mistakes Forgetting to multiply � in factorization. Misplacing the signs of numbers when splitting the middle term. Skipping the step of factoring out the common term. Real-World Applications Quadratic equations appear in: Projectile motion in physics (height of a thrown object over time) Area optimization problems (e.g., fencing a rectangular field) Profit maximization in business scenarios Practice Problems (Increasing Difficulty) � � � � � Guidance for Mastery Always identify �, �, and � first. Try factorization first; if it fails, use the quadratic formula. Practice recognizing patterns (perfect squares, simple factors). Apply problems to real-life examples to strengthen understanding.