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Simplifying 80 = 0.05s2 + 1.1s Reorder the terms: 80 = 1.1s + 0.05s2 Solving 80 = 1.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 80 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2 Combine like terms: 1.1s + -1.1s = 0.0 80 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 80 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 80 + -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'. -1600 + 22s + s2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 22s + 1600 + s2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 22s + s2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 22s + s2 = 0 + 1600 22s + s2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 22s + s2 = 1600 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 = 1600 + 121 Reorder the terms: 121 + 22s + s2 = 1600 + 121 Combine like terms: 1600 + 121 = 1721 121 + 22s + s2 = 1721 Factor a perfect square on the left side: (s + 11)(s + 11) = 1721 Calculate the square root of the right side: 41.484937025 Break this problem into two subproblems by setting (s + 11) equal to 41.484937025 and -41.484937025.Subproblem 1
s + 11 = 41.484937025 Simplifying s + 11 = 41.484937025 Reorder the terms: 11 + s = 41.484937025 Solving 11 + s = 41.484937025 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 = 41.484937025 + -11 Combine like terms: 11 + -11 = 0 0 + s = 41.484937025 + -11 s = 41.484937025 + -11 Combine like terms: 41.484937025 + -11 = 30.484937025 s = 30.484937025 Simplifying s = 30.484937025Subproblem 2
s + 11 = -41.484937025 Simplifying s + 11 = -41.484937025 Reorder the terms: 11 + s = -41.484937025 Solving 11 + s = -41.484937025 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 = -41.484937025 + -11 Combine like terms: 11 + -11 = 0 0 + s = -41.484937025 + -11 s = -41.484937025 + -11 Combine like terms: -41.484937025 + -11 = -52.484937025 s = -52.484937025 Simplifying s = -52.484937025Solution
The solution to the problem is based on the solutions from the subproblems. s = {30.484937025, -52.484937025}
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