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Simplifying s2 + -2s + -2 = 0 Reorder the terms: -2 + -2s + s2 = 0 Solving -2 + -2s + 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 + -2s + 2 + s2 = 0 + 2 Reorder the terms: -2 + 2 + -2s + s2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2s + s2 = 0 + 2 -2s + s2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2s + s2 = 2 The s term is -2s. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2s + 1 + s2 = 2 + 1 Reorder the terms: 1 + -2s + s2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2s + s2 = 3 Factor a perfect square on the left side: (s + -1)(s + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (s + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
s + -1 = 1.732050808 Simplifying s + -1 = 1.732050808 Reorder the terms: -1 + s = 1.732050808 Solving -1 + s = 1.732050808 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + s = 1.732050808 + 1 s = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 s = 2.732050808 Simplifying s = 2.732050808Subproblem 2
s + -1 = -1.732050808 Simplifying s + -1 = -1.732050808 Reorder the terms: -1 + s = -1.732050808 Solving -1 + s = -1.732050808 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + s = -1.732050808 + 1 s = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 s = -0.732050808 Simplifying s = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.732050808, -0.732050808}
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