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Simplifying s2 = 11s + 11 Reorder the terms: s2 = 11 + 11s Solving s2 = 11 + 11s Solving for variable 's'. Reorder the terms: -11 + -11s + s2 = 11 + 11s + -11 + -11s Reorder the terms: -11 + -11s + s2 = 11 + -11 + 11s + -11s Combine like terms: 11 + -11 = 0 -11 + -11s + s2 = 0 + 11s + -11s -11 + -11s + s2 = 11s + -11s Combine like terms: 11s + -11s = 0 -11 + -11s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -11s + 11 + s2 = 0 + 11 Reorder the terms: -11 + 11 + -11s + s2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -11s + s2 = 0 + 11 -11s + s2 = 0 + 11 Combine like terms: 0 + 11 = 11 -11s + s2 = 11 The s term is -11s. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11s + 30.25 + s2 = 11 + 30.25 Reorder the terms: 30.25 + -11s + s2 = 11 + 30.25 Combine like terms: 11 + 30.25 = 41.25 30.25 + -11s + s2 = 41.25 Factor a perfect square on the left side: (s + -5.5)(s + -5.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (s + -5.5) equal to 6.422616289 and -6.422616289.Subproblem 1
s + -5.5 = 6.422616289 Simplifying s + -5.5 = 6.422616289 Reorder the terms: -5.5 + s = 6.422616289 Solving -5.5 + s = 6.422616289 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + s = 6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + s = 6.422616289 + 5.5 s = 6.422616289 + 5.5 Combine like terms: 6.422616289 + 5.5 = 11.922616289 s = 11.922616289 Simplifying s = 11.922616289Subproblem 2
s + -5.5 = -6.422616289 Simplifying s + -5.5 = -6.422616289 Reorder the terms: -5.5 + s = -6.422616289 Solving -5.5 + s = -6.422616289 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + s = -6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + s = -6.422616289 + 5.5 s = -6.422616289 + 5.5 Combine like terms: -6.422616289 + 5.5 = -0.922616289 s = -0.922616289 Simplifying s = -0.922616289Solution
The solution to the problem is based on the solutions from the subproblems. s = {11.922616289, -0.922616289}
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