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Simplifying 45s2 + 50s + 6 = 0 Reorder the terms: 6 + 50s + 45s2 = 0 Solving 6 + 50s + 45s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.1333333333 + 1.111111111s + s2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 1.111111111s + -0.1333333333 + s2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 1.111111111s + s2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 1.111111111s + s2 = 0 + -0.1333333333 1.111111111s + s2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 1.111111111s + s2 = -0.1333333333 The s term is 1.111111111s. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111s + 0.3086419752 + s2 = -0.1333333333 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111s + s2 = -0.1333333333 + 0.3086419752 Combine like terms: -0.1333333333 + 0.3086419752 = 0.1753086419 0.3086419752 + 1.111111111s + s2 = 0.1753086419 Factor a perfect square on the left side: (s + 0.5555555555)(s + 0.5555555555) = 0.1753086419 Calculate the square root of the right side: 0.418698748 Break this problem into two subproblems by setting (s + 0.5555555555) equal to 0.418698748 and -0.418698748.Subproblem 1
s + 0.5555555555 = 0.418698748 Simplifying s + 0.5555555555 = 0.418698748 Reorder the terms: 0.5555555555 + s = 0.418698748 Solving 0.5555555555 + s = 0.418698748 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + s = 0.418698748 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + s = 0.418698748 + -0.5555555555 s = 0.418698748 + -0.5555555555 Combine like terms: 0.418698748 + -0.5555555555 = -0.1368568075 s = -0.1368568075 Simplifying s = -0.1368568075Subproblem 2
s + 0.5555555555 = -0.418698748 Simplifying s + 0.5555555555 = -0.418698748 Reorder the terms: 0.5555555555 + s = -0.418698748 Solving 0.5555555555 + s = -0.418698748 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + s = -0.418698748 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + s = -0.418698748 + -0.5555555555 s = -0.418698748 + -0.5555555555 Combine like terms: -0.418698748 + -0.5555555555 = -0.9742543035 s = -0.9742543035 Simplifying s = -0.9742543035Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.1368568075, -0.9742543035}
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