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Simplifying -1s + -2 = -7s2 Reorder the terms: -2 + -1s = -7s2 Solving -2 + -1s = -7s2 Solving for variable 's'. Combine like terms: -7s2 + 7s2 = 0 -2 + -1s + 7s2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -0.1428571429s + s2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.1428571429s + 0.2857142857 + s2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.1428571429s + s2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.1428571429s + s2 = 0 + 0.2857142857 -0.1428571429s + s2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.1428571429s + s2 = 0.2857142857 The s term is -0.1428571429s. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429s + 0.005102040819 + s2 = 0.2857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429s + s2 = 0.2857142857 + 0.005102040819 Combine like terms: 0.2857142857 + 0.005102040819 = 0.290816326519 0.005102040819 + -0.1428571429s + s2 = 0.290816326519 Factor a perfect square on the left side: (s + -0.07142857145)(s + -0.07142857145) = 0.290816326519 Calculate the square root of the right side: 0.539273888 Break this problem into two subproblems by setting (s + -0.07142857145) equal to 0.539273888 and -0.539273888.Subproblem 1
s + -0.07142857145 = 0.539273888 Simplifying s + -0.07142857145 = 0.539273888 Reorder the terms: -0.07142857145 + s = 0.539273888 Solving -0.07142857145 + s = 0.539273888 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + s = 0.539273888 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + s = 0.539273888 + 0.07142857145 s = 0.539273888 + 0.07142857145 Combine like terms: 0.539273888 + 0.07142857145 = 0.61070245945 s = 0.61070245945 Simplifying s = 0.61070245945Subproblem 2
s + -0.07142857145 = -0.539273888 Simplifying s + -0.07142857145 = -0.539273888 Reorder the terms: -0.07142857145 + s = -0.539273888 Solving -0.07142857145 + s = -0.539273888 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + s = -0.539273888 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + s = -0.539273888 + 0.07142857145 s = -0.539273888 + 0.07142857145 Combine like terms: -0.539273888 + 0.07142857145 = -0.46784531655 s = -0.46784531655 Simplifying s = -0.46784531655Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.61070245945, -0.46784531655}
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