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Simplifying s2 + 11s = 30 Reorder the terms: 11s + s2 = 30 Solving 11s + s2 = 30 Solving for variable 's'. Reorder the terms: -30 + 11s + s2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 11s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 11s + 30 + s2 = 0 + 30 Reorder the terms: -30 + 30 + 11s + s2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11s + s2 = 0 + 30 11s + s2 = 0 + 30 Combine like terms: 0 + 30 = 30 11s + s2 = 30 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 = 30 + 30.25 Reorder the terms: 30.25 + 11s + s2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + 11s + s2 = 60.25 Factor a perfect square on the left side: (s + 5.5)(s + 5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (s + 5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
s + 5.5 = 7.762087348 Simplifying s + 5.5 = 7.762087348 Reorder the terms: 5.5 + s = 7.762087348 Solving 5.5 + s = 7.762087348 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 = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + s = 7.762087348 + -5.5 s = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 s = 2.262087348 Simplifying s = 2.262087348Subproblem 2
s + 5.5 = -7.762087348 Simplifying s + 5.5 = -7.762087348 Reorder the terms: 5.5 + s = -7.762087348 Solving 5.5 + s = -7.762087348 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 = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + s = -7.762087348 + -5.5 s = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 s = -13.262087348 Simplifying s = -13.262087348Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.262087348, -13.262087348}
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