x(x + 2) = 168.

["How to Solve the Equation x(x + 2) = 168: Step-by-Step Guide", "Solving quadratic equations is a fundamental skill in algebra, and one common form students frequently encounter is equations in the expanded product format, such as x(x + 2) = 168. Whether you're a high school student tackling algebra or someone looking to brush up on math fundamentals, understanding how to solve this equation step-by-step can make learning efficient and empowering. In this article, we dive deep into solving x(x + 2) = 168, explain the process, and share practical tips for mastering quadratic equations.", "---", "### Step 1: Expand the Equation", "We start by simplifying the left-hand side of the equation:", "[\nx(x + 2) = 168\n]", "Apply the distributive property (also known as the FOIL method):", "[\nx^2 + 2x = 168\n]", "Now, move all terms to one side to set the equation to zero:", "[\nx^2 + 2x - 168 = 0\n]", "This is now a standard quadratic equation in the form ax² + bx + c = 0, where a = 1, b = 2, and c = -168.", "---", "### Step 2: Factor the Quadratic Equation (If Possible)", "To solve x² + 2x - 168 = 0, we look for two numbers that multiply to -168 (product) and add to 2 (sum).", "After testing factor pairs:", "[\n14 \ imes (-12) = -168 \quad \ ext{and} \quad 14 + (-12) = 2\n]", "These numbers work, so we can factor the equation as:", "[\n(x + 14)(x - 12) = 0\n]", "---", "### Step 3: Apply the Zero Product Property", "Set each factor equal to zero:", "[\nx + 14 = 0 \quad \Rightarrow \quad x = -14\n]\n[\nx - 12 = 0 \quad \Rightarrow \quad x = 12\n]", "Thus, the solutions to x(x + 2) = 168 are:", "[\nx = -14 \quad \ ext{and} \quad x = 12\n]", "---", "### Step 4: Verify the Solutions", "Plug the values back into the original equation to confirm:", "- For x = 12:\n (12(12 + 2) = 12 \ imes 14 = 168) ✓", "- For x = -14:\n (-14(-14 + 2) = -14 \ imes (-12) = 168) ✓", "Both solutions satisfy the equation.", "---", "### Why Understanding This Equation Matters", "Equations like x(x + 2) = 168 are more than just algebra exercises—they model real-world scenarios such as area calculations, business profit models, and physics problems. Mastering how to solve them strengthens problem-solving and logical reasoning skills, which are essential across science, engineering, and economics fields.", "---", "### Tips for Mastering This Type of Problem", "- Always expand products before solving: Expanding simplifies the equation and reveals standard quadratic form.\n- Learn factor pairs efficiently: Knowing common factor pairs of constants (like -168) speeds up factoring.\n- Use the Zero Product Property: A powerful technique for solving zeroed equations.\n- Practice repeatedly: Try other equations with different numbers to build speed and confidence.\n- Check each solution: Substituting back ensures no errors and reinforces accuracy.", "---", "Conclusion", "Solving x(x + 2) = 168 not only gives the answers x = -14 and x = 12 but also illustrates core algebraic strategies: expanding, factoring, applying key theorems, and verifying. With consistent practice, quadratic equations become manageable—and even intuitive—tools in everyday math and höheres Niveau (higher-level) studies.", "---", "Key Takeaways:", "- Expand: x(x + 2) → x² + 2x\n- Form: x² + 2x – 168 = 0\n- Solve by factoring: (x + 14)(x – 12) = 0\n- Solutions: x = –14 or x = 12\n- Always verify by substitution", "Start mastering these steps today—your algebra skills will thank you!", "---", "See Also:\n- How to solve quadratic equations quickly\n- Factoring quadratics: step-by-step guide\n- Real-world applications of x(x + 2) models\n- Best resources for learning algebra", "Keywords: equation solving, quadratic equations, x(x + 2) = 168, algebra tutorials, factoring, zero product property, solving quadratics, math practice problems."]