So 2x² = 348,480 → x² = 174,240 → x = √174,240 ≈ 417.47

["How to Solve the Equation 2x² = 348,480: Step-by-Step Guide with Solution (x ≈ 417.47)", "Solving quadratic equations is a fundamental skill in algebra, widely used in math, physics, economics, and engineering. One simple but classic example is solving the equation 2x² = 348,480. In this article, we’ll walk through the step-by-step process to find the value of ( x ), with the final result approximately equal to 417.47.", "---", "### Understanding the Equation", "We start with the equation:", "[\n2x^2 = 348,480\n]", "Our goal is to isolate (x), which requires us to simplify the equation and apply square roots.", "---", "### Step 1: Divide Both Sides by 2", "To eliminate the coefficient of (x^2), divide both sides of the equation by 2:", "[\nx^2 = \frac{348,480}{2} = 174,240\n]", "---", "### Step 2: Take the Square Root", "Next, solve for (x) by taking the square root of both sides:", "[\nx = \sqrt{174,240}\n]", "Since 174,240 is not a perfect square, we compute its approximate square root. Using a calculator:", "[\n\sqrt{174,240} \approx 417.47\n]", "Remember that square roots yield both positive and negative solutions:", "[\nx \approx \pm 417.47\n]", "---", "### Why This Matters", "Quadratic equations often arise in real-world applications such as:", "- Calculating dimensions from area or volume\n- Modeling financial returns over time\n- Determining optimal values in physics\n- Solving business and engineering problems", "In this case, simplifying complex expressions like (2x^2 = 348,480) quickly leads to precise numerical approximations.", "---", "### Final Answer", "[\nx = \sqrt{174,240} \approx 417.47\n]", "---", "Takeaway: Solving equations step-by-step ensures precision, especially when variables are squared. Whether you're a student mastering algebra or a professional applying math in practical tasks, understanding how to simplify equations and compute roots accurately is essential.", "If you found this guide helpful, share it to help others master solving quadratic equations!", "---", "Keywords:\n2x² = 348480, solve x, quadratic equation, square root, x ≈ 417.47, step-by-step math, algebra tutorial, simplify equation, real-world equations."]