A rectangular swimming pool measures 25 meters by 10 meters and is surrounded by a uniform deck of width \(x\) meters. If the total area is 600 square meters, find \(x\).

["Find the Widest Uniform Deck Width Surrounding a 25m x 10m Rectangular Pool", "If you’re planning to build a rectangular pool measuring 25 meters by 10 meters and add a uniform concrete deck of width (x) meters around it, understanding how to calculate the total area is essential for budgeting, design, and construction. In this article, we explore how to determine the deck width (x) when the total area—pool plus deck—is 600 square meters.", "---", "### Understanding the Pool and Deck Layout", "The pool itself has dimensions 25m (length) by 10m (width). A uniform deck surrounds the pool on all sides, increasing each dimension by (x) meters:", "- Total length including deck: (25 + 2x) meters (adding (x) on both ends)\n- Total width including deck: (10 + 2x) meters", "Thus, the total surface area (pool + deck) is:", "[\nA = (25 + 2x)(10 + 2x)\n]", "We’re told this total area equals 600 square meters:", "[\n(25 + 2x)(10 + 2x) = 600\n]", "---", "### Step-by-Step Algebra to Solve for (x)", "Expand the left-hand side:", "[\n(25 + 2x)(10 + 2x) = 25 \cdot 10 + 25 \cdot 2x + 2x \cdot 10 + 2x \cdot 2x = 250 + 50x + 20x + 4x^2 = 4x^2 + 70x + 250\n]", "Set equal to 600:", "[\n4x^2 + 70x + 250 = 600\n]", "Subtract 600 from both sides:", "[\n4x^2 + 70x + 250 - 600 = 0\n]\n[\n4x^2 + 70x - 350 = 0\n]", "Divide through by 2 to simplify:", "[\n2x^2 + 35x - 175 = 0\n]", "---", "### Solving the Quadratic Equation", "We now solve (2x^2 + 35x - 175 = 0) using the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Where (a = 2), (b = 35), (c = -175):", "[\nx = \frac{-35 \pm \sqrt{35^2 - 4(2)(-175)}}{2(2)} = \frac{-35 \pm \sqrt{1225 + 1400}}{4} = \frac{-35 \pm \sqrt{2625}}{4}\n]", "Simplify (\sqrt{2625}):", "[\n\sqrt{2625} = \sqrt{25 \ imes 105} = 5\sqrt{105}\n]", "So,", "[\nx = \frac{-35 \pm 5\sqrt{105}}{4}\n]", "We discard the negative solution since width cannot be negative:", "[\nx = \frac{-35 + 5\sqrt{105}}{4}\n]", "Calculate approximate value:", "[\n\sqrt{105} \approx 10.247 \quad \Rightarrow \quad 5\sqrt{105} \approx 51.235\n]\n[\nx \approx \frac{-35 + 51.235}{4} = \frac{16.235}{4} \approx 4.06 \ ext{ meters}\n]", "---", "### Final Answer and Summary", "The uniform deck width (x) that completes a total pool and deck area of 600 square meters is approximately:", "[\n\boxed{x = \frac{-35 + 5\sqrt{105}}{4} \approx 4.06 \ ext{ meters}}\n]", "---", "### Practical Tips", "- Always double-check dimensions for safety, accessibility, and building code compliance.\n- Slight deck width adjustments can affect water flow, tile layout, and shading.\n- Using exact form (x = \frac{-35 + 5\sqrt{105}}{4}) ensures precision for blueprint planning or engineering.", "By carefully balancing pool size and deck expansion, you create an inviting, functional outdoor space—ideal for relaxation and recreation.", "---", "Keywords: rectangular pool size 25x10 meters, uniform deck width, total area 600 square meters, find deck width, pool deck calculation, quadratic equation pool, swimming pool deck design"]