x = [-2 ± 24] / 2. Possible positive root, x = (24 - 2) / 2 = 11.

["Understanding the Equation: x = [-2 ± 24] / 2 – Solving the Positive Root", "When faced with an expression like ( x = \frac{-2 \pm 24}{2} ), many students instantly calculate the two possible values without fully understanding how the ± sign works. In this article, we’ll explore step-by-step how to solve this equation and highlight the positive root—specifically, why ( x = \frac{24 - 2}{2} = 11 ) is one of the two correct answers.", "---", "### What Does the Equation x = [-2 ± 24] / 2 Mean?", "The expression ( x = \frac{-2 \pm 24}{2} ) uses the mathematical convention of the ± symbol, which represents two scenarios:", "- The + case: ( +24 )\n- The – case: ( -24 )", "This means we are solving two linear equations simultaneously:", "1. ( x = \frac{-2 + 24}{2} )\n2. ( x = \frac{-2 - 24}{2} )", "---", "### Step-by-Step Calculation", "Let’s compute both roots clearly:", "#### First root (positive case):\n[\nx = \frac{-2 + 24}{2} = \frac{22}{2} = 11\n]", "#### Second root (negative case):\n[\nx = \frac{-2 - 24}{2} = \frac{-26}{2} = -13\n]", "So, the two solutions are:", "- ( x = 11 ) ✅ (positive root)\n- ( x = -13 )", "---", "### Why Is ( x = \frac{24 - 2}{2} = 11 ) the Positive Solution?", "While the ± symbol gives two symmetric solutions, picking the one with the minus before the 24 may seem counterintuitive—until you recognize this:", "- The expression can be rewritten as two separate equations as shown above.\n- The root obtained by subtracting 24 first gives the positive value.\n- This aligns with intuitive number ordering—positive solutions typically come from subtracting a large number from a moderate one before dividing if the result remains positive.", "Thus, choosing ( \frac{24 - 2}{2} ) directly yields the larger (positive) solution:\n[\nx = \frac{24 - 2}{2} = \frac{22}{2} = 11\n]", "---", "### Real-World Applications and Importance", "Understanding how to properly interpret and solve equations with ± signs is essential in algebra, physics, and engineering. These expressions often model real-world situations like:", "- Calculating average outcomes with positive and negative deviations\n- Determining range values in data analysis\n- Solving quadratic simplifications via factoring or completing the square", "Mastering the ± interpretation ensures accurate results, especially when only positive values make practical sense.", "---", "### Summary", "- The equation ( x = \frac{-2 \pm 24}{2} ) gives two roots: 11 and –13\n- The positive root comes from ( x = \frac{24 - 2}{2} = 11 ) due to division distributing over subtraction\n- Always evaluate both cases—positive and negative—but recognize symmetry in the solution\n- This foundational skill strengthens problem-solving across STEM fields", "---", "### Want to Learn More?", "Check out our full guide on solving linear equations with absolute values and the power of the ± rule — your key to confident algebra!", "---", "Key Takeaway:\nWhen solving ( x = \frac{-2 \pm 24}{2} ), the positive root is ( x = 11 ) obtained from ( \frac{24 - 2}{2} ), illustrating how careful sign handling leads to accurate solutions."]