Esto se simplifica a 2w^2 = 72, por lo que w^2 = 36, y w = 6 metros.
["How to Solve 2w² = 72: A Simple Step-by-Step Guide and Real-World Application", "Understanding quadratic equations can seem tricky at first, but with simple steps, even complex problems become easy to solve. In this article, we’ll explain how to simplify the equation 2w² = 72, find w², and ultimately determine that w = 6 meters. Whether you’re a student tackling math homework or brushing up on fundamentals, this guide helps demystify the process behind the solution.", "### Simplifying the Equation: From 2w² = 72 to w² = 36", "The first step in solving any quadratic equation is simplification. Starting with:", "[\n2w^2 = 72\n]", "To isolate the term with the variable, divide both sides by 2:", "[\nw^2 = \frac{72}{2} = 36\n]", "This simplification reduces the equation to a clear, straightforward form:", "[\nw^2 = 36\n]", "### Solving for w: Taking the Square Root", "Now that we know w² = 36, the next step is finding w by taking the square root of both sides. Since squaring returns both positive and negative roots, mathematically:", "[\nw = \pm\sqrt{36} = \pm 6\n]", "However, in practical applications—especially those involving physical measurements such as dimensions—a positive value applies. Since w represents a length (in meters), we discard the negative solution.", "Thus,\n[\nw = 6 \ ext{ meters}\n]", "### Real-Life Example: Calculating Area", "Imagine you’re designing a square garden and know its area is 72 square meters. If you define side length w as one of the dimensions, the area formula becomes:", "[\n\ ext{Area} = w^2\n]", "But if the problem states total area equals 2w² = 72, solving gives:", "[\nw^2 = 36 \quad \Rightarrow \quad w = 6 \ ext{ meters}\n]", "This confirms the side length of the garden for accurate planning.", "### Summary", "- Start with: (2w^2 = 72)\n- Simplify: (w^2 = 36)\n- Solve: (w = \sqrt{36} = 6)\n- Final result: w = 6 meters", "---", "Understanding how to simplify and solve quadratic equations like 2w² = 72 is essential in school subjects such as algebra and in fields like architecture, physics, and engineering. Always simplify step-by-step, consider context clues for value selection, and apply the square root carefully—especially when representing real-world quantities.", "Mastering these fundamentals makes even advanced math feel manageable and highly useful in daily life and professional work."]
