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Simplifying s2 + 18s + -34 = 49 Reorder the terms: -34 + 18s + s2 = 49 Solving -34 + 18s + s2 = 49 Solving for variable 's'. Reorder the terms: -34 + -49 + 18s + s2 = 49 + -49 Combine like terms: -34 + -49 = -83 -83 + 18s + s2 = 49 + -49 Combine like terms: 49 + -49 = 0 -83 + 18s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + 18s + 83 + s2 = 0 + 83 Reorder the terms: -83 + 83 + 18s + s2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + 18s + s2 = 0 + 83 18s + s2 = 0 + 83 Combine like terms: 0 + 83 = 83 18s + s2 = 83 The s term is 18s. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18s + 81 + s2 = 83 + 81 Reorder the terms: 81 + 18s + s2 = 83 + 81 Combine like terms: 83 + 81 = 164 81 + 18s + s2 = 164 Factor a perfect square on the left side: (s + 9)(s + 9) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (s + 9) equal to 12.806248475 and -12.806248475.Subproblem 1
s + 9 = 12.806248475 Simplifying s + 9 = 12.806248475 Reorder the terms: 9 + s = 12.806248475 Solving 9 + s = 12.806248475 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = 12.806248475 + -9 Combine like terms: 9 + -9 = 0 0 + s = 12.806248475 + -9 s = 12.806248475 + -9 Combine like terms: 12.806248475 + -9 = 3.806248475 s = 3.806248475 Simplifying s = 3.806248475Subproblem 2
s + 9 = -12.806248475 Simplifying s + 9 = -12.806248475 Reorder the terms: 9 + s = -12.806248475 Solving 9 + s = -12.806248475 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + s = -12.806248475 + -9 Combine like terms: 9 + -9 = 0 0 + s = -12.806248475 + -9 s = -12.806248475 + -9 Combine like terms: -12.806248475 + -9 = -21.806248475 s = -21.806248475 Simplifying s = -21.806248475Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.806248475, -21.806248475}
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