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Simplifying s2 + -18s = 49 Reorder the terms: -18s + s2 = 49 Solving -18s + s2 = 49 Solving for variable 's'. Reorder the terms: -49 + -18s + s2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -18s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -18s + 49 + s2 = 0 + 49 Reorder the terms: -49 + 49 + -18s + s2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -18s + s2 = 0 + 49 -18s + s2 = 0 + 49 Combine like terms: 0 + 49 = 49 -18s + s2 = 49 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 = 49 + 81 Reorder the terms: 81 + -18s + s2 = 49 + 81 Combine like terms: 49 + 81 = 130 81 + -18s + s2 = 130 Factor a perfect square on the left side: (s + -9)(s + -9) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (s + -9) equal to 11.401754251 and -11.401754251.Subproblem 1
s + -9 = 11.401754251 Simplifying s + -9 = 11.401754251 Reorder the terms: -9 + s = 11.401754251 Solving -9 + s = 11.401754251 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 = 11.401754251 + 9 Combine like terms: -9 + 9 = 0 0 + s = 11.401754251 + 9 s = 11.401754251 + 9 Combine like terms: 11.401754251 + 9 = 20.401754251 s = 20.401754251 Simplifying s = 20.401754251Subproblem 2
s + -9 = -11.401754251 Simplifying s + -9 = -11.401754251 Reorder the terms: -9 + s = -11.401754251 Solving -9 + s = -11.401754251 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 = -11.401754251 + 9 Combine like terms: -9 + 9 = 0 0 + s = -11.401754251 + 9 s = -11.401754251 + 9 Combine like terms: -11.401754251 + 9 = -2.401754251 s = -2.401754251 Simplifying s = -2.401754251Solution
The solution to the problem is based on the solutions from the subproblems. s = {20.401754251, -2.401754251}
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