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Simplifying 75 = 0.05s2 + 1.1s Reorder the terms: 75 = 1.1s + 0.05s2 Solving 75 = 1.1s + 0.05s2 Solving for variable 's'. Reorder the terms: 75 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2 Combine like terms: 1.1s + -1.1s = 0.0 75 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2 75 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2 Combine like terms: 0.05s2 + -0.05s2 = 0.00 75 + -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'. -1500 + 22s + s2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + 22s + 1500 + s2 = 0 + 1500 Reorder the terms: -1500 + 1500 + 22s + s2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + 22s + s2 = 0 + 1500 22s + s2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 22s + s2 = 1500 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 = 1500 + 121 Reorder the terms: 121 + 22s + s2 = 1500 + 121 Combine like terms: 1500 + 121 = 1621 121 + 22s + s2 = 1621 Factor a perfect square on the left side: (s + 11)(s + 11) = 1621 Calculate the square root of the right side: 40.261644278 Break this problem into two subproblems by setting (s + 11) equal to 40.261644278 and -40.261644278.Subproblem 1
s + 11 = 40.261644278 Simplifying s + 11 = 40.261644278 Reorder the terms: 11 + s = 40.261644278 Solving 11 + s = 40.261644278 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 = 40.261644278 + -11 Combine like terms: 11 + -11 = 0 0 + s = 40.261644278 + -11 s = 40.261644278 + -11 Combine like terms: 40.261644278 + -11 = 29.261644278 s = 29.261644278 Simplifying s = 29.261644278Subproblem 2
s + 11 = -40.261644278 Simplifying s + 11 = -40.261644278 Reorder the terms: 11 + s = -40.261644278 Solving 11 + s = -40.261644278 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 = -40.261644278 + -11 Combine like terms: 11 + -11 = 0 0 + s = -40.261644278 + -11 s = -40.261644278 + -11 Combine like terms: -40.261644278 + -11 = -51.261644278 s = -51.261644278 Simplifying s = -51.261644278Solution
The solution to the problem is based on the solutions from the subproblems. s = {29.261644278, -51.261644278}
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