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Simplifying s2 + 12s + -11 = 35 Reorder the terms: -11 + 12s + s2 = 35 Solving -11 + 12s + s2 = 35 Solving for variable 's'. Reorder the terms: -11 + -35 + 12s + s2 = 35 + -35 Combine like terms: -11 + -35 = -46 -46 + 12s + s2 = 35 + -35 Combine like terms: 35 + -35 = 0 -46 + 12s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 12s + 46 + s2 = 0 + 46 Reorder the terms: -46 + 46 + 12s + s2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 12s + s2 = 0 + 46 12s + s2 = 0 + 46 Combine like terms: 0 + 46 = 46 12s + s2 = 46 The s term is 12s. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12s + 36 + s2 = 46 + 36 Reorder the terms: 36 + 12s + s2 = 46 + 36 Combine like terms: 46 + 36 = 82 36 + 12s + s2 = 82 Factor a perfect square on the left side: (s + 6)(s + 6) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (s + 6) equal to 9.055385138 and -9.055385138.Subproblem 1
s + 6 = 9.055385138 Simplifying s + 6 = 9.055385138 Reorder the terms: 6 + s = 9.055385138 Solving 6 + s = 9.055385138 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = 9.055385138 + -6 Combine like terms: 6 + -6 = 0 0 + s = 9.055385138 + -6 s = 9.055385138 + -6 Combine like terms: 9.055385138 + -6 = 3.055385138 s = 3.055385138 Simplifying s = 3.055385138Subproblem 2
s + 6 = -9.055385138 Simplifying s + 6 = -9.055385138 Reorder the terms: 6 + s = -9.055385138 Solving 6 + s = -9.055385138 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = -9.055385138 + -6 Combine like terms: 6 + -6 = 0 0 + s = -9.055385138 + -6 s = -9.055385138 + -6 Combine like terms: -9.055385138 + -6 = -15.055385138 s = -15.055385138 Simplifying s = -15.055385138Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.055385138, -15.055385138}
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