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Simplifying s2 + 24s + 31 = 0 Reorder the terms: 31 + 24s + s2 = 0 Solving 31 + 24s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 24s + -31 + s2 = 0 + -31 Reorder the terms: 31 + -31 + 24s + s2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 24s + s2 = 0 + -31 24s + s2 = 0 + -31 Combine like terms: 0 + -31 = -31 24s + s2 = -31 The s term is 24s. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24s + 144 + s2 = -31 + 144 Reorder the terms: 144 + 24s + s2 = -31 + 144 Combine like terms: -31 + 144 = 113 144 + 24s + s2 = 113 Factor a perfect square on the left side: (s + 12)(s + 12) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (s + 12) equal to 10.630145813 and -10.630145813.Subproblem 1
s + 12 = 10.630145813 Simplifying s + 12 = 10.630145813 Reorder the terms: 12 + s = 10.630145813 Solving 12 + s = 10.630145813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + s = 10.630145813 + -12 Combine like terms: 12 + -12 = 0 0 + s = 10.630145813 + -12 s = 10.630145813 + -12 Combine like terms: 10.630145813 + -12 = -1.369854187 s = -1.369854187 Simplifying s = -1.369854187Subproblem 2
s + 12 = -10.630145813 Simplifying s + 12 = -10.630145813 Reorder the terms: 12 + s = -10.630145813 Solving 12 + s = -10.630145813 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + s = -10.630145813 + -12 Combine like terms: 12 + -12 = 0 0 + s = -10.630145813 + -12 s = -10.630145813 + -12 Combine like terms: -10.630145813 + -12 = -22.630145813 s = -22.630145813 Simplifying s = -22.630145813Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.369854187, -22.630145813}
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