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Simplifying S2 + 50S + 6 = 0 Reorder the terms: 6 + 50S + S2 = 0 Solving 6 + 50S + S2 = 0 Solving for variable 'S'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 50S + -6 + S2 = 0 + -6 Reorder the terms: 6 + -6 + 50S + S2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 50S + S2 = 0 + -6 50S + S2 = 0 + -6 Combine like terms: 0 + -6 = -6 50S + S2 = -6 The S term is 50S. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50S + 625 + S2 = -6 + 625 Reorder the terms: 625 + 50S + S2 = -6 + 625 Combine like terms: -6 + 625 = 619 625 + 50S + S2 = 619 Factor a perfect square on the left side: (S + 25)(S + 25) = 619 Calculate the square root of the right side: 24.879710609 Break this problem into two subproblems by setting (S + 25) equal to 24.879710609 and -24.879710609.Subproblem 1
S + 25 = 24.879710609 Simplifying S + 25 = 24.879710609 Reorder the terms: 25 + S = 24.879710609 Solving 25 + S = 24.879710609 Solving for variable 'S'. Move all terms containing S to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + S = 24.879710609 + -25 Combine like terms: 25 + -25 = 0 0 + S = 24.879710609 + -25 S = 24.879710609 + -25 Combine like terms: 24.879710609 + -25 = -0.120289391 S = -0.120289391 Simplifying S = -0.120289391Subproblem 2
S + 25 = -24.879710609 Simplifying S + 25 = -24.879710609 Reorder the terms: 25 + S = -24.879710609 Solving 25 + S = -24.879710609 Solving for variable 'S'. Move all terms containing S to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + S = -24.879710609 + -25 Combine like terms: 25 + -25 = 0 0 + S = -24.879710609 + -25 S = -24.879710609 + -25 Combine like terms: -24.879710609 + -25 = -49.879710609 S = -49.879710609 Simplifying S = -49.879710609Solution
The solution to the problem is based on the solutions from the subproblems. S = {-0.120289391, -49.879710609}
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