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Simplifying (s + 3)(s + 5) + s(10 + -1s) = 11s + 1 Reorder the terms: (3 + s)(s + 5) + s(10 + -1s) = 11s + 1 Reorder the terms: (3 + s)(5 + s) + s(10 + -1s) = 11s + 1 Multiply (3 + s) * (5 + s) (3(5 + s) + s(5 + s)) + s(10 + -1s) = 11s + 1 ((5 * 3 + s * 3) + s(5 + s)) + s(10 + -1s) = 11s + 1 ((15 + 3s) + s(5 + s)) + s(10 + -1s) = 11s + 1 (15 + 3s + (5 * s + s * s)) + s(10 + -1s) = 11s + 1 (15 + 3s + (5s + s2)) + s(10 + -1s) = 11s + 1 Combine like terms: 3s + 5s = 8s (15 + 8s + s2) + s(10 + -1s) = 11s + 1 15 + 8s + s2 + (10 * s + -1s * s) = 11s + 1 15 + 8s + s2 + (10s + -1s2) = 11s + 1 Reorder the terms: 15 + 8s + 10s + s2 + -1s2 = 11s + 1 Combine like terms: 8s + 10s = 18s 15 + 18s + s2 + -1s2 = 11s + 1 Combine like terms: s2 + -1s2 = 0 15 + 18s + 0 = 11s + 1 15 + 18s = 11s + 1 Reorder the terms: 15 + 18s = 1 + 11s Solving 15 + 18s = 1 + 11s Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11s' to each side of the equation. 15 + 18s + -11s = 1 + 11s + -11s Combine like terms: 18s + -11s = 7s 15 + 7s = 1 + 11s + -11s Combine like terms: 11s + -11s = 0 15 + 7s = 1 + 0 15 + 7s = 1 Add '-15' to each side of the equation. 15 + -15 + 7s = 1 + -15 Combine like terms: 15 + -15 = 0 0 + 7s = 1 + -15 7s = 1 + -15 Combine like terms: 1 + -15 = -14 7s = -14 Divide each side by '7'. s = -2 Simplifying s = -2
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