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Home » Recompute: 3n² + 7n - 220 = 0 - go-checkin.com

Recompute: 3n² + 7n - 220 = 0 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A rectangular garden measures 20 meters by 15 meters. If a path of uniform width is built around the garden, increasing the total area to 396 square meters, what is the width of the path?

📌 Let the width of the path be w meters. New dimensions are (20 + 2w) by (15 + 2w).

📌 New area = (20 + 2w)(15 + 2w) = 396.

📌 Expanding, 300 + 70w + 4w² = 396.

📌 Simplifying, 4w² + 70w - 96 = 0.

📌 Solving this quadratic using the quadratic formula, w = [-70 ± √(70² - 4*4*(-96))] / (2*4).

📌 Discriminant = 4900 + 1536 = 6436, √6436 ≈ 80.23.

📌 w = [-70 ± 80.23] / 8. Possible positive root, w = (80.23 - 70) / 8 ≈ 1.28.

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