Solve for \(x\) in the equation \(3x^2 - 12x + 9 = 0\).

["How to Solve for (x) in the Equation (3x^2 - 12x + 9 = 0) – A Step-by-Step Guide with Explanations", "Solving quadratic equations is a fundamental skill in algebra, and the equation (3x^2 - 12x + 9 = 0) is a classic example that students and math learners frequently encounter. Whether you're a high school student, a college beginner, or someone brushing up on algebra, understanding how to solve this equation helps build strong problem-solving skills.", "In this article, we’ll walk through the process of solving (3x^2 - 12x + 9 = 0) step by step, explain common techniques, and highlight best practices so you can confidently solve similar quadratic equations in the future.", "---", "### Step 1: Simplify the Equation", "The given equation is:", "[\n3x^2 - 12x + 9 = 0\n]", "Notice that all terms are divisible by 3. Dividing the entire equation by 3 simplifies the computation:", "[\nx^2 - 4x + 3 = 0\n]", "Simplifying the equation reduces the complexity without changing the solutions — a smart first step in solving quadratics.", "---", "### Step 2: Identify Coefficients for the Quadratic Formula", "For the simplified equation:", "[\nx^2 - 4x + 3 = 0\n]", "We identify the standard coefficients:\n- (a = 1) (coefficient of (x^2))\n- (b = -4) (coefficient of (x))\n- (c = 3) (constant term)", "The quadratic formula is the go-to method for solving any quadratic equation:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "---", "### Step 3: Calculate the Discriminant", "Before plugging into the formula, compute the discriminant:", "[\n\Delta = b^2 - 4ac = (-4)^2 - 4(1)(3) = 16 - 12 = 4\n]", "Since (\Delta = 4 > 0), there are two distinct real solutions. The square root of 4 is 2, so the square root term is manageable.", "---", "### Step 4: Apply the Quadratic Formula", "Now substitute (a), (b), and (\Delta) into the quadratic formula:", "[\nx = \frac{-(-4) \pm \sqrt{4}}{2(1)} = \frac{4 \pm 2}{2}\n]", "This gives two solutions:", "1. (x = \frac{4 + 2}{2} = \frac{6}{2} = 3)\n2. (x = \frac{4 - 2}{2} = \frac{2}{2} = 1)", "---", "### Step 5: Verify the Solutions", "It’s always wise to check the solutions by plugging them back into the original equation (3x^2 - 12x + 9 = 0):", "- For (x = 3):\n (3(3)^2 - 12(3) + 9 = 27 - 36 + 9 = 0) ✅", "- For (x = 1):\n (3(1)^2 - 12(1) + 9 = 3 - 12 + 9 = 0) ✅", "Both solutions satisfy the equation, confirming correctness.", "---", "### Why Solving (3x^2 - 12x + 9 = 0) Matters", "Beyond memorizing steps, understanding this equation reinforces key algebraic concepts:\n- Factoring: This quadratic factors neatly as ((x - 3)(x - 1) = 0), revealing roots directly.\n- Symmetry and real-world applications: Quadratic models often represent motion, profit, or area — solving for (x) means finding key points in real-world scenarios.\n- Building foundation for advanced topics: Successfully solving quadratics prepares learners for more complex subjects like calculus and engineering.", "---", "### Summary", "The equation (3x^2 - 12x + 9 = 0), when simplified to (x^2 - 4x + 3 = 0), yields two real solutions: (x = 1) and (x = 3). Using the quadratic formula, discriminant analysis, and verification ensures a thorough and accurate solution process.", "With practice, solving quadratic equations becomes intuitive — empowering you to tackle math challenges confidently.", "---", "Keywords: solve (3x^2 - 12x + 9 = 0), quadratic formula step-by-step, solve quadratics, algebraic solutions, discriminant interpretation, real roots cubic equation solve", "Meta Description: Learn how to solve (3x^2 - 12x + 9 = 0) using the quadratic formula, step-by-step explanations, simplified methods, and real-world applications. Ideal for students and math learners."]