This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here is an exercise on the topic of solving quadratic equations by factoring. Question: Solve the quadratic equation: x² + 5x + 6 = 0 Solution: Step 1: We need to find two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Step 2: Rewrite the middle term (5x) using these two numbers: x² + 2x + 3x + 6 = 0. Step 3: Factor by grouping. Group the first two terms and the last two terms: (x² + 2x) + (3x + 6) = 0. Step 4: Factor out the greatest common factor from each group: x(x + 2) + 3(x + 2) = 0. Step 5: Notice that (x + 2) is a common factor. Factor it out: (x + 2)(x + 3) = 0. Step 6: Set each factor equal to zero and solve for x: x + 2 = 0 ⟹ x = -2 x + 3 = 0 ⟹ x = -3 The solutions are x = -2 and x = -3. Final Answer: The solutions to the equation x² + 5x + 6 = 0 are x = -2 and x = -3. Send me the next one 📸