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Simplifying s2 + 0.2s + -0.08 = 0 Reorder the terms: -0.08 + 0.2s + s2 = 0 Solving -0.08 + 0.2s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.2s + 0.08 + s2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.2s + s2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.2s + s2 = 0 + 0.08 0.2s + s2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.2s + s2 = 0.08 The s term is 0.2s. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2s + 0.01 + s2 = 0.08 + 0.01 Reorder the terms: 0.01 + 0.2s + s2 = 0.08 + 0.01 Combine like terms: 0.08 + 0.01 = 0.09 0.01 + 0.2s + s2 = 0.09 Factor a perfect square on the left side: (s + 0.1)(s + 0.1) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (s + 0.1) equal to 0.3 and -0.3.Subproblem 1
s + 0.1 = 0.3 Simplifying s + 0.1 = 0.3 Reorder the terms: 0.1 + s = 0.3 Solving 0.1 + s = 0.3 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + s = 0.3 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + s = 0.3 + -0.1 s = 0.3 + -0.1 Combine like terms: 0.3 + -0.1 = 0.2 s = 0.2 Simplifying s = 0.2Subproblem 2
s + 0.1 = -0.3 Simplifying s + 0.1 = -0.3 Reorder the terms: 0.1 + s = -0.3 Solving 0.1 + s = -0.3 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + s = -0.3 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + s = -0.3 + -0.1 s = -0.3 + -0.1 Combine like terms: -0.3 + -0.1 = -0.4 s = -0.4 Simplifying s = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.2, -0.4}
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