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Simplifying 95 = 0.05s2 + 1.1s Reorder the terms: 95 = 1.1s + 0.05s2 Solving 95 = 1.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 95 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2 Combine like terms: 1.1s + -1.1s = 0.0 95 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 95 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 95 + -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'. -1900 + 22s + s2 = 0 Move the constant term to the right: Add '1900' to each side of the equation. -1900 + 22s + 1900 + s2 = 0 + 1900 Reorder the terms: -1900 + 1900 + 22s + s2 = 0 + 1900 Combine like terms: -1900 + 1900 = 0 0 + 22s + s2 = 0 + 1900 22s + s2 = 0 + 1900 Combine like terms: 0 + 1900 = 1900 22s + s2 = 1900 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 = 1900 + 121 Reorder the terms: 121 + 22s + s2 = 1900 + 121 Combine like terms: 1900 + 121 = 2021 121 + 22s + s2 = 2021 Factor a perfect square on the left side: (s + 11)(s + 11) = 2021 Calculate the square root of the right side: 44.955533586 Break this problem into two subproblems by setting (s + 11) equal to 44.955533586 and -44.955533586.Subproblem 1
s + 11 = 44.955533586 Simplifying s + 11 = 44.955533586 Reorder the terms: 11 + s = 44.955533586 Solving 11 + s = 44.955533586 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 = 44.955533586 + -11 Combine like terms: 11 + -11 = 0 0 + s = 44.955533586 + -11 s = 44.955533586 + -11 Combine like terms: 44.955533586 + -11 = 33.955533586 s = 33.955533586 Simplifying s = 33.955533586Subproblem 2
s + 11 = -44.955533586 Simplifying s + 11 = -44.955533586 Reorder the terms: 11 + s = -44.955533586 Solving 11 + s = -44.955533586 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 = -44.955533586 + -11 Combine like terms: 11 + -11 = 0 0 + s = -44.955533586 + -11 s = -44.955533586 + -11 Combine like terms: -44.955533586 + -11 = -55.955533586 s = -55.955533586 Simplifying s = -55.955533586Solution
The solution to the problem is based on the solutions from the subproblems. s = {33.955533586, -55.955533586}
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