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Simplifying 5s + 8(2s + -8) * s = 8 Reorder the terms: 5s + 8(-8 + 2s) * s = 8 Reorder the terms for easier multiplication: 5s + 8s(-8 + 2s) = 8 5s + (-8 * 8s + 2s * 8s) = 8 5s + (-64s + 16s2) = 8 Combine like terms: 5s + -64s = -59s -59s + 16s2 = 8 Solving -59s + 16s2 = 8 Solving for variable 's'. Reorder the terms: -8 + -59s + 16s2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -59s + 16s2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -3.6875s + s2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.6875s + 0.5 + s2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.6875s + s2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.6875s + s2 = 0 + 0.5 -3.6875s + s2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.6875s + s2 = 0.5 The s term is -3.6875s. Take half its coefficient (-1.84375). Square it (3.399414063) and add it to both sides. Add '3.399414063' to each side of the equation. -3.6875s + 3.399414063 + s2 = 0.5 + 3.399414063 Reorder the terms: 3.399414063 + -3.6875s + s2 = 0.5 + 3.399414063 Combine like terms: 0.5 + 3.399414063 = 3.899414063 3.399414063 + -3.6875s + s2 = 3.899414063 Factor a perfect square on the left side: (s + -1.84375)(s + -1.84375) = 3.899414063 Calculate the square root of the right side: 1.97469341 Break this problem into two subproblems by setting (s + -1.84375) equal to 1.97469341 and -1.97469341.Subproblem 1
s + -1.84375 = 1.97469341 Simplifying s + -1.84375 = 1.97469341 Reorder the terms: -1.84375 + s = 1.97469341 Solving -1.84375 + s = 1.97469341 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + s = 1.97469341 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + s = 1.97469341 + 1.84375 s = 1.97469341 + 1.84375 Combine like terms: 1.97469341 + 1.84375 = 3.81844341 s = 3.81844341 Simplifying s = 3.81844341Subproblem 2
s + -1.84375 = -1.97469341 Simplifying s + -1.84375 = -1.97469341 Reorder the terms: -1.84375 + s = -1.97469341 Solving -1.84375 + s = -1.97469341 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.84375' to each side of the equation. -1.84375 + 1.84375 + s = -1.97469341 + 1.84375 Combine like terms: -1.84375 + 1.84375 = 0.00000 0.00000 + s = -1.97469341 + 1.84375 s = -1.97469341 + 1.84375 Combine like terms: -1.97469341 + 1.84375 = -0.13094341 s = -0.13094341 Simplifying s = -0.13094341Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.81844341, -0.13094341}
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