Question: Find the largest value of $ x $ that satisfies the equation $ 2x^2 - 10x + 12 = 0 $.
["Finding the Largest Value of $ x $ That Satisfies $ 2x^2 - 10x + 12 = 0 $", "When solving quadratic equations, one common task is identifying the largest (or smallest) solution. In this article, we’ll explore how to find the largest value of $ x $ that satisfies the equation:", "$$\n2x^2 - 10x + 12 = 0\n$$", "### Step 1: Simplify the Equation", "Before solving, simplify the equation by dividing every term by 2:", "$$\nx^2 - 5x + 6 = 0\n$$", "This simplified form makes root calculation easier using factoring or the quadratic formula.", "### Step 2: Factor the Quadratic", "Try factoring the quadratic expression:", "$$\nx^2 - 5x + 6 = (x - 2)(x - 3) = 0\n$$", "Setting each factor equal to zero gives the solutions:", "$$\nx - 2 = 0 \Rightarrow x = 2\n$$\n$$\nx - 3 = 0 \Rightarrow x = 3\n$$", "### Step 3: Identify the Largest Solution", "From the solutions $ x = 2 $ and $ x = 3 $, the largest value is:", "$$\n\boxed{3}\n$$", "### Bonus: Verify Using the Quadratic Formula (Optional)", "For completeness, apply the quadratic formula:", "$$\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n$$", "Here, $ a = 1 $, $ b = -5 $, $ c = 6 $:", "$$\nx = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(6)}}{2(1)} = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2}\n$$", "So the two solutions are:", "$$\nx = \frac{5 + 1}{2} = 3 \quad \ ext{and} \quad x = \frac{5 - 1}{2} = 2\n$$", "Again, confirming the largest value is $ \boxed{3} $.", "---", "### SEO Optimization Notes", "- Target Keywords: find largest x, solve quadratic equation, quadratic formula solution\n- Header Tags: Use <h1> for the main title, <h2> for subsections like “Step 1: Simplify the Equation” and “Step 2: Factor the Quadratic”\n- Meta Description: “Learn how to find the largest value of $ x $ satisfying $ 2x^2 - 10x + 12 = 0 $ using factoring and the quadratic formula.”\n- Internal and external links (if applicable) to related geometry or algebra content\n- Keyword density: Natural integration of “largest value,” “solve quadratic,” and “equation solutions”", "This article helps beginners understand how to systematically solve a quadratic equation and identify the largest root—optimized for search visibility and clear, actionable explanation."]
