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Simplifying 2s2 + -59s + 17 = 0 Reorder the terms: 17 + -59s + 2s2 = 0 Solving 17 + -59s + 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'. 8.5 + -29.5s + s2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -29.5s + -8.5 + s2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -29.5s + s2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -29.5s + s2 = 0 + -8.5 -29.5s + s2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -29.5s + s2 = -8.5 The s term is -29.5s. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5s + 217.5625 + s2 = -8.5 + 217.5625 Reorder the terms: 217.5625 + -29.5s + s2 = -8.5 + 217.5625 Combine like terms: -8.5 + 217.5625 = 209.0625 217.5625 + -29.5s + s2 = 209.0625 Factor a perfect square on the left side: (s + -14.75)(s + -14.75) = 209.0625 Calculate the square root of the right side: 14.458993741 Break this problem into two subproblems by setting (s + -14.75) equal to 14.458993741 and -14.458993741.Subproblem 1
s + -14.75 = 14.458993741 Simplifying s + -14.75 = 14.458993741 Reorder the terms: -14.75 + s = 14.458993741 Solving -14.75 + s = 14.458993741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + s = 14.458993741 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + s = 14.458993741 + 14.75 s = 14.458993741 + 14.75 Combine like terms: 14.458993741 + 14.75 = 29.208993741 s = 29.208993741 Simplifying s = 29.208993741Subproblem 2
s + -14.75 = -14.458993741 Simplifying s + -14.75 = -14.458993741 Reorder the terms: -14.75 + s = -14.458993741 Solving -14.75 + s = -14.458993741 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + s = -14.458993741 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + s = -14.458993741 + 14.75 s = -14.458993741 + 14.75 Combine like terms: -14.458993741 + 14.75 = 0.291006259 s = 0.291006259 Simplifying s = 0.291006259Solution
The solution to the problem is based on the solutions from the subproblems. s = {29.208993741, 0.291006259}
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