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Home » $T_n = S_n-1$ (append 2 to a string ending in 3) - High Altitude Science

$T_n = S_n-1$ (append 2 to a string ending in 3) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The total area equation is \( (30 + 2x)(20 + 2x) = 936 \).

📌 Expanding: \( 600 + 60x + 40x + 4x^2 = 936 \).

📌 Simplifying: \( 4x^2 + 100x + 600 = 936 \).

📌 Subtract 936 from both sides: \( 4x^2 + 100x - 336 = 0 \).

📌 Divide the entire equation by 4: \( x^2 + 25x - 84 = 0 \).

📌 Solve the quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1, b = 25, c = -84 \).

📌 Calculate the discriminant: \( 25^2 - 4 \times 1 \times (-84) = 625 + 336 = 961 \).

📌 Find the square root of the discriminant: \( \sqrt{961} = 31 \).

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