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Simplifying 100 = 0.05s2 + 1.1s Reorder the terms: 100 = 1.1s + 0.05s2 Solving 100 = 1.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 100 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2 Combine like terms: 1.1s + -1.1s = 0.0 100 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 100 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 100 + -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'. -2000 + 22s + s2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 22s + 2000 + s2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 22s + s2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 22s + s2 = 0 + 2000 22s + s2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 22s + s2 = 2000 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 = 2000 + 121 Reorder the terms: 121 + 22s + s2 = 2000 + 121 Combine like terms: 2000 + 121 = 2121 121 + 22s + s2 = 2121 Factor a perfect square on the left side: (s + 11)(s + 11) = 2121 Calculate the square root of the right side: 46.054315759 Break this problem into two subproblems by setting (s + 11) equal to 46.054315759 and -46.054315759.Subproblem 1
s + 11 = 46.054315759 Simplifying s + 11 = 46.054315759 Reorder the terms: 11 + s = 46.054315759 Solving 11 + s = 46.054315759 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 = 46.054315759 + -11 Combine like terms: 11 + -11 = 0 0 + s = 46.054315759 + -11 s = 46.054315759 + -11 Combine like terms: 46.054315759 + -11 = 35.054315759 s = 35.054315759 Simplifying s = 35.054315759Subproblem 2
s + 11 = -46.054315759 Simplifying s + 11 = -46.054315759 Reorder the terms: 11 + s = -46.054315759 Solving 11 + s = -46.054315759 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 = -46.054315759 + -11 Combine like terms: 11 + -11 = 0 0 + s = -46.054315759 + -11 s = -46.054315759 + -11 Combine like terms: -46.054315759 + -11 = -57.054315759 s = -57.054315759 Simplifying s = -57.054315759Solution
The solution to the problem is based on the solutions from the subproblems. s = {35.054315759, -57.054315759}
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