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Simplifying s2 + 6s + 2 = 0 Reorder the terms: 2 + 6s + s2 = 0 Solving 2 + 6s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6s + -2 + s2 = 0 + -2 Reorder the terms: 2 + -2 + 6s + s2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6s + s2 = 0 + -2 6s + s2 = 0 + -2 Combine like terms: 0 + -2 = -2 6s + s2 = -2 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 = -2 + 9 Reorder the terms: 9 + 6s + s2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6s + s2 = 7 Factor a perfect square on the left side: (s + 3)(s + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (s + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
s + 3 = 2.645751311 Simplifying s + 3 = 2.645751311 Reorder the terms: 3 + s = 2.645751311 Solving 3 + s = 2.645751311 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 = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + s = 2.645751311 + -3 s = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 s = -0.354248689 Simplifying s = -0.354248689Subproblem 2
s + 3 = -2.645751311 Simplifying s + 3 = -2.645751311 Reorder the terms: 3 + s = -2.645751311 Solving 3 + s = -2.645751311 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 = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + s = -2.645751311 + -3 s = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 s = -5.645751311 Simplifying s = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.354248689, -5.645751311}
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