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Simplifying 14s2 + 29s + 10 = 0 Reorder the terms: 10 + 29s + 14s2 = 0 Solving 10 + 29s + 14s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.7142857143 + 2.071428571s + s2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 2.071428571s + -0.7142857143 + s2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 2.071428571s + s2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 2.071428571s + s2 = 0 + -0.7142857143 2.071428571s + s2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 2.071428571s + s2 = -0.7142857143 The s term is 2.071428571s. Take half its coefficient (1.035714286). Square it (1.072704082) and add it to both sides. Add '1.072704082' to each side of the equation. 2.071428571s + 1.072704082 + s2 = -0.7142857143 + 1.072704082 Reorder the terms: 1.072704082 + 2.071428571s + s2 = -0.7142857143 + 1.072704082 Combine like terms: -0.7142857143 + 1.072704082 = 0.3584183677 1.072704082 + 2.071428571s + s2 = 0.3584183677 Factor a perfect square on the left side: (s + 1.035714286)(s + 1.035714286) = 0.3584183677 Calculate the square root of the right side: 0.598680522 Break this problem into two subproblems by setting (s + 1.035714286) equal to 0.598680522 and -0.598680522.Subproblem 1
s + 1.035714286 = 0.598680522 Simplifying s + 1.035714286 = 0.598680522 Reorder the terms: 1.035714286 + s = 0.598680522 Solving 1.035714286 + s = 0.598680522 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.035714286' to each side of the equation. 1.035714286 + -1.035714286 + s = 0.598680522 + -1.035714286 Combine like terms: 1.035714286 + -1.035714286 = 0.000000000 0.000000000 + s = 0.598680522 + -1.035714286 s = 0.598680522 + -1.035714286 Combine like terms: 0.598680522 + -1.035714286 = -0.437033764 s = -0.437033764 Simplifying s = -0.437033764Subproblem 2
s + 1.035714286 = -0.598680522 Simplifying s + 1.035714286 = -0.598680522 Reorder the terms: 1.035714286 + s = -0.598680522 Solving 1.035714286 + s = -0.598680522 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.035714286' to each side of the equation. 1.035714286 + -1.035714286 + s = -0.598680522 + -1.035714286 Combine like terms: 1.035714286 + -1.035714286 = 0.000000000 0.000000000 + s = -0.598680522 + -1.035714286 s = -0.598680522 + -1.035714286 Combine like terms: -0.598680522 + -1.035714286 = -1.634394808 s = -1.634394808 Simplifying s = -1.634394808Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.437033764, -1.634394808}
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