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Simplifying (0.1 + x)(0.05 + x) = 0 Multiply (0.1 + x) * (0.05 + x) (0.1(0.05 + x) + x(0.05 + x)) = 0 ((0.05 * 0.1 + x * 0.1) + x(0.05 + x)) = 0 ((0.005 + 0.1x) + x(0.05 + x)) = 0 (0.005 + 0.1x + (0.05 * x + x * x)) = 0 (0.005 + 0.1x + (0.05x + x2)) = 0 Combine like terms: 0.1x + 0.05x = 0.15x (0.005 + 0.15x + x2) = 0 Solving 0.005 + 0.15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.005' to each side of the equation. 0.005 + 0.15x + -0.005 + x2 = 0 + -0.005 Reorder the terms: 0.005 + -0.005 + 0.15x + x2 = 0 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + 0.15x + x2 = 0 + -0.005 0.15x + x2 = 0 + -0.005 Combine like terms: 0 + -0.005 = -0.005 0.15x + x2 = -0.005 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = -0.005 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = -0.005 + 0.005625 Combine like terms: -0.005 + 0.005625 = 0.000625 0.005625 + 0.15x + x2 = 0.000625 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = 0.000625 Calculate the square root of the right side: 0.025 Break this problem into two subproblems by setting (x + 0.075) equal to 0.025 and -0.025.Subproblem 1
x + 0.075 = 0.025 Simplifying x + 0.075 = 0.025 Reorder the terms: 0.075 + x = 0.025 Solving 0.075 + x = 0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = 0.025 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = 0.025 + -0.075 x = 0.025 + -0.075 Combine like terms: 0.025 + -0.075 = -0.05 x = -0.05 Simplifying x = -0.05Subproblem 2
x + 0.075 = -0.025 Simplifying x + 0.075 = -0.025 Reorder the terms: 0.075 + x = -0.025 Solving 0.075 + x = -0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + x = -0.025 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + x = -0.025 + -0.075 x = -0.025 + -0.075 Combine like terms: -0.025 + -0.075 = -0.1 x = -0.1 Simplifying x = -0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.05, -0.1}
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