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Simplifying 2s2 + 17s + 27 = 0 Reorder the terms: 27 + 17s + 2s2 = 0 Solving 27 + 17s + 2s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 8.5s + s2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 8.5s + -13.5 + s2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 8.5s + s2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 8.5s + s2 = 0 + -13.5 8.5s + s2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 8.5s + s2 = -13.5 The s term is 8.5s. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5s + 18.0625 + s2 = -13.5 + 18.0625 Reorder the terms: 18.0625 + 8.5s + s2 = -13.5 + 18.0625 Combine like terms: -13.5 + 18.0625 = 4.5625 18.0625 + 8.5s + s2 = 4.5625 Factor a perfect square on the left side: (s + 4.25)(s + 4.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (s + 4.25) equal to 2.136000936 and -2.136000936.Subproblem 1
s + 4.25 = 2.136000936 Simplifying s + 4.25 = 2.136000936 Reorder the terms: 4.25 + s = 2.136000936 Solving 4.25 + s = 2.136000936 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + s = 2.136000936 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + s = 2.136000936 + -4.25 s = 2.136000936 + -4.25 Combine like terms: 2.136000936 + -4.25 = -2.113999064 s = -2.113999064 Simplifying s = -2.113999064Subproblem 2
s + 4.25 = -2.136000936 Simplifying s + 4.25 = -2.136000936 Reorder the terms: 4.25 + s = -2.136000936 Solving 4.25 + s = -2.136000936 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + s = -2.136000936 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + s = -2.136000936 + -4.25 s = -2.136000936 + -4.25 Combine like terms: -2.136000936 + -4.25 = -6.386000936 s = -6.386000936 Simplifying s = -6.386000936Solution
The solution to the problem is based on the solutions from the subproblems. s = {-2.113999064, -6.386000936}
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