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Simplifying 200 = 0.05s2 + 1.1s Reorder the terms: 200 = 1.1s + 0.05s2 Solving 200 = 1.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 200 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2 Combine like terms: 1.1s + -1.1s = 0.0 200 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 200 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 200 + -1.1s + -0.05s2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -4000 + 22s + s2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 22s + 4000 + s2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 22s + s2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 22s + s2 = 0 + 4000 22s + s2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 22s + s2 = 4000 The s term is 22s. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22s + 121 + s2 = 4000 + 121 Reorder the terms: 121 + 22s + s2 = 4000 + 121 Combine like terms: 4000 + 121 = 4121 121 + 22s + s2 = 4121 Factor a perfect square on the left side: (s + 11)(s + 11) = 4121 Calculate the square root of the right side: 64.195015383 Break this problem into two subproblems by setting (s + 11) equal to 64.195015383 and -64.195015383.Subproblem 1
s + 11 = 64.195015383 Simplifying s + 11 = 64.195015383 Reorder the terms: 11 + s = 64.195015383 Solving 11 + s = 64.195015383 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = 64.195015383 + -11 Combine like terms: 11 + -11 = 0 0 + s = 64.195015383 + -11 s = 64.195015383 + -11 Combine like terms: 64.195015383 + -11 = 53.195015383 s = 53.195015383 Simplifying s = 53.195015383Subproblem 2
s + 11 = -64.195015383 Simplifying s + 11 = -64.195015383 Reorder the terms: 11 + s = -64.195015383 Solving 11 + s = -64.195015383 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + s = -64.195015383 + -11 Combine like terms: 11 + -11 = 0 0 + s = -64.195015383 + -11 s = -64.195015383 + -11 Combine like terms: -64.195015383 + -11 = -75.195015383 s = -75.195015383 Simplifying s = -75.195015383Solution
The solution to the problem is based on the solutions from the subproblems. s = {53.195015383, -75.195015383}
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