\(2(2x^2 + 6x^2 + 3x^2) = 94 \rightarrow 22x^2 = 94 \rightarrow x^2 = \frac{94}{22} = \frac{47}{11}\).
["How to Solve the Equation: A Step-by-Step Guide to (2(2x^2 + 6x^2 + 3x^2) = 94)", "Solving quadratic equations is a fundamental skill in algebra, and understanding step-by-step methods helps ensure accuracy. One common problem you might encounter involves simplifying expressions with like terms, applying algebraic rules, and isolating variables. Let’s break down the equation (2(2x^2 + 6x^2 + 3x^2) = 94) and walk through its solution.", "---", "### Understanding the Equation", "Start with:\n[\n2(2x^2 + 6x^2 + 3x^2) = 94\n]", "This equation combines like terms inside the parentheses before multiplying by 2. Understanding this structure is key to moving forward correctly.", "---", "### Step 1: Simplify Inside the Parentheses", "Combine the coefficients of the terms with (x^2):\n[\n2x^2 + 6x^2 + 3x^2 = (2 + 6 + 3)x^2 = 11x^2\n]", "So the equation becomes:\n[\n2(11x^2) = 94\n]", "---", "### Step 2: Distribute the 2", "Multiply both sides by 2:\n[\n22x^2 = 94\n]", "---", "### Step 3: Isolate (x^2)", "Divide both sides by 22:\n[\nx^2 = \frac{94}{22}\n]", "Simplify the fraction:\n[\nx^2 = \frac{47}{11}\n]", "---", "### Step 4: Solve for (x) (Optional)", "If desired, take square roots to find (x):\n[\nx = \pm \sqrt{\frac{47}{11}} = \pm \frac{\sqrt{517}}{11}\n]", "(Note: The problem ends at (x^2 = \frac{47}{11}), so the roots are expressed implicitly in squared form.)", "---", "### Why This Problem Matters\nMastering step-by-step simplification and equation solving builds confidence in tackling more complex algebraic expressions. Proper simplification (like combining like terms) ensures accurate results and faster problem-solving.", "---", "### Key Takeaways\n- Combine like terms early before applying multiplication.\n- Distribute operations carefully and isolate variables systematically.\n- Simplify fractions to their lowest terms.\n- Use calculator or rationalization when working with square roots.", "---", "If you’re studying quadratic equations or practice algebraic simplification, this structured approach ensures clarity and correctness. Keep practicing—strong algebra skills open the door to advanced math!", "---", "Keywords for SEO:\nsolve 2(2x² + 6x² + 3x²) = 94, simplify quadratic expressions, step-by-step solving 22x² = 94, x² = 94/22, algebraic equations with like terms, quadratic equation calculation, intermediate algebra tutorials, solving 2(ax² + bx²) = c, simplify expressions to isolate x²", "---", "Master your algebra—by cracking equations one step at a time!"]
