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Simplifying s2 + 6s + 6 = 0 Reorder the terms: 6 + 6s + s2 = 0 Solving 6 + 6s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6s + -6 + s2 = 0 + -6 Reorder the terms: 6 + -6 + 6s + s2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6s + s2 = 0 + -6 6s + s2 = 0 + -6 Combine like terms: 0 + -6 = -6 6s + s2 = -6 The s term is 6s. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6s + 9 + s2 = -6 + 9 Reorder the terms: 9 + 6s + s2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + 6s + s2 = 3 Factor a perfect square on the left side: (s + 3)(s + 3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (s + 3) equal to 1.732050808 and -1.732050808.Subproblem 1
s + 3 = 1.732050808 Simplifying s + 3 = 1.732050808 Reorder the terms: 3 + s = 1.732050808 Solving 3 + s = 1.732050808 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + s = 1.732050808 + -3 s = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 s = -1.267949192 Simplifying s = -1.267949192Subproblem 2
s + 3 = -1.732050808 Simplifying s + 3 = -1.732050808 Reorder the terms: 3 + s = -1.732050808 Solving 3 + s = -1.732050808 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + s = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + s = -1.732050808 + -3 s = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 s = -4.732050808 Simplifying s = -4.732050808Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.267949192, -4.732050808}
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