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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Let the first integer be \( n \). Then the next consecutive integer is \( n + 1 \).

📌 The equation is \( n^2 + (n + 1)^2 = 85 \).

📌 Expand and simplify: \( n^2 + n^2 + 2n + 1 = 85 \), \( 2n^2 + 2n + 1 = 85 \).

📌 Subtract 85 from both sides: \( 2n^2 + 2n + 1 - 85 = 0 \), \( 2n^2 + 2n - 84 = 0 \).

📌 Divide the whole equation by 2: \( n^2 + n - 42 = 0 \).

📌 Factor the quadratic: \( (n + 7)(n - 6) = 0 \).

📌 Solve for \( n \): \( n = -7 \) or \( n = 6 \).

📌 The consecutive integers are \(-7, -6\) or \(6, 7\).

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