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Home » Step 2: Count favorable outcomes — sequences of 5 rolls using exactly two distinct values. - Midis

Step 2: Count favorable outcomes — sequences of 5 rolls using exactly two distinct values. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \[ (x + 5)(x - 3) = 120 \]

📌 \[ x^2 + 2x - 15 = 120 \]

📌 \[ x^2 + 2x - 135 = 0 \]

📌 Solve using quadratic formula:

📌 \[ x = \frac{-2 \pm \sqrt{4 + 540}}{2} = \frac{-2 \pm \sqrt{544}}{2} \]

📌 \[ \sqrt{544} = \sqrt{16 \times 34} = 4\sqrt{34} \]

📌 \[ x = \frac{-2 + 4\sqrt{34}}{2} = -1 + 2\sqrt{34} \]

📌 \( \sqrt{34} \approx 5.831 \), so \( x \approx -1 + 11.662 = 10.662 \)

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