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Simplifying 3s + s + s2 + 2 = 0 Reorder the terms: 2 + 3s + s + s2 = 0 Combine like terms: 3s + s = 4s 2 + 4s + s2 = 0 Solving 2 + 4s + 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 + 4s + -2 + s2 = 0 + -2 Reorder the terms: 2 + -2 + 4s + s2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4s + s2 = 0 + -2 4s + s2 = 0 + -2 Combine like terms: 0 + -2 = -2 4s + s2 = -2 The s term is 4s. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4s + 4 + s2 = -2 + 4 Reorder the terms: 4 + 4s + s2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + 4s + s2 = 2 Factor a perfect square on the left side: (s + 2)(s + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (s + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
s + 2 = 1.414213562 Simplifying s + 2 = 1.414213562 Reorder the terms: 2 + s = 1.414213562 Solving 2 + s = 1.414213562 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + s = 1.414213562 + -2 s = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 s = -0.585786438 Simplifying s = -0.585786438Subproblem 2
s + 2 = -1.414213562 Simplifying s + 2 = -1.414213562 Reorder the terms: 2 + s = -1.414213562 Solving 2 + s = -1.414213562 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + s = -1.414213562 + -2 s = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 s = -3.414213562 Simplifying s = -3.414213562Solution
The solution to the problem is based on the solutions from the subproblems. s = {-0.585786438, -3.414213562}
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