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Simplifying 20 = 0.0052s2 + 0.13s Reorder the terms: 20 = 0.13s + 0.0052s2 Solving 20 = 0.13s + 0.0052s2 Solving for variable 's'. Reorder the terms: 20 + -0.13s + -0.0052s2 = 0.13s + -0.13s + 0.0052s2 + -0.0052s2 Combine like terms: 0.13s + -0.13s = 0.00 20 + -0.13s + -0.0052s2 = 0.00 + 0.0052s2 + -0.0052s2 20 + -0.13s + -0.0052s2 = 0.0052s2 + -0.0052s2 Combine like terms: 0.0052s2 + -0.0052s2 = 0.0000 20 + -0.13s + -0.0052s2 = 0.0000 Begin completing the square. Divide all terms by -0.0052 the coefficient of the squared term: Divide each side by '-0.0052'. -3846.153846 + 25s + s2 = 0 Move the constant term to the right: Add '3846.153846' to each side of the equation. -3846.153846 + 25s + 3846.153846 + s2 = 0 + 3846.153846 Reorder the terms: -3846.153846 + 3846.153846 + 25s + s2 = 0 + 3846.153846 Combine like terms: -3846.153846 + 3846.153846 = 0.000000 0.000000 + 25s + s2 = 0 + 3846.153846 25s + s2 = 0 + 3846.153846 Combine like terms: 0 + 3846.153846 = 3846.153846 25s + s2 = 3846.153846 The s term is 25s. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25s + 156.25 + s2 = 3846.153846 + 156.25 Reorder the terms: 156.25 + 25s + s2 = 3846.153846 + 156.25 Combine like terms: 3846.153846 + 156.25 = 4002.403846 156.25 + 25s + s2 = 4002.403846 Factor a perfect square on the left side: (s + 12.5)(s + 12.5) = 4002.403846 Calculate the square root of the right side: 63.26455442 Break this problem into two subproblems by setting (s + 12.5) equal to 63.26455442 and -63.26455442.Subproblem 1
s + 12.5 = 63.26455442 Simplifying s + 12.5 = 63.26455442 Reorder the terms: 12.5 + s = 63.26455442 Solving 12.5 + s = 63.26455442 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + s = 63.26455442 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + s = 63.26455442 + -12.5 s = 63.26455442 + -12.5 Combine like terms: 63.26455442 + -12.5 = 50.76455442 s = 50.76455442 Simplifying s = 50.76455442Subproblem 2
s + 12.5 = -63.26455442 Simplifying s + 12.5 = -63.26455442 Reorder the terms: 12.5 + s = -63.26455442 Solving 12.5 + s = -63.26455442 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + s = -63.26455442 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + s = -63.26455442 + -12.5 s = -63.26455442 + -12.5 Combine like terms: -63.26455442 + -12.5 = -75.76455442 s = -75.76455442 Simplifying s = -75.76455442Solution
The solution to the problem is based on the solutions from the subproblems. s = {50.76455442, -75.76455442}
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