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Simplifying s2 + 18s + -12 = 0 Reorder the terms: -12 + 18s + s2 = 0 Solving -12 + 18s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 18s + 12 + s2 = 0 + 12 Reorder the terms: -12 + 12 + 18s + s2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 18s + s2 = 0 + 12 18s + s2 = 0 + 12 Combine like terms: 0 + 12 = 12 18s + s2 = 12 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 = 12 + 81 Reorder the terms: 81 + 18s + s2 = 12 + 81 Combine like terms: 12 + 81 = 93 81 + 18s + s2 = 93 Factor a perfect square on the left side: (s + 9)(s + 9) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (s + 9) equal to 9.643650761 and -9.643650761.Subproblem 1
s + 9 = 9.643650761 Simplifying s + 9 = 9.643650761 Reorder the terms: 9 + s = 9.643650761 Solving 9 + s = 9.643650761 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 = 9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + s = 9.643650761 + -9 s = 9.643650761 + -9 Combine like terms: 9.643650761 + -9 = 0.643650761 s = 0.643650761 Simplifying s = 0.643650761Subproblem 2
s + 9 = -9.643650761 Simplifying s + 9 = -9.643650761 Reorder the terms: 9 + s = -9.643650761 Solving 9 + s = -9.643650761 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 = -9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + s = -9.643650761 + -9 s = -9.643650761 + -9 Combine like terms: -9.643650761 + -9 = -18.643650761 s = -18.643650761 Simplifying s = -18.643650761Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.643650761, -18.643650761}
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