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Simplifying (0.15 + x)(x + 0.05) = 0 Reorder the terms: (0.15 + x)(0.05 + x) = 0 Multiply (0.15 + x) * (0.05 + x) (0.15(0.05 + x) + x(0.05 + x)) = 0 ((0.05 * 0.15 + x * 0.15) + x(0.05 + x)) = 0 ((0.0075 + 0.15x) + x(0.05 + x)) = 0 (0.0075 + 0.15x + (0.05 * x + x * x)) = 0 (0.0075 + 0.15x + (0.05x + x2)) = 0 Combine like terms: 0.15x + 0.05x = 0.2x (0.0075 + 0.2x + x2) = 0 Solving 0.0075 + 0.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0075' to each side of the equation. 0.0075 + 0.2x + -0.0075 + x2 = 0 + -0.0075 Reorder the terms: 0.0075 + -0.0075 + 0.2x + x2 = 0 + -0.0075 Combine like terms: 0.0075 + -0.0075 = 0.0000 0.0000 + 0.2x + x2 = 0 + -0.0075 0.2x + x2 = 0 + -0.0075 Combine like terms: 0 + -0.0075 = -0.0075 0.2x + x2 = -0.0075 The x term is 0.2x. 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. 0.2x + 0.01 + x2 = -0.0075 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -0.0075 + 0.01 Combine like terms: -0.0075 + 0.01 = 0.0025 0.01 + 0.2x + x2 = 0.0025 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + 0.1) equal to 0.05 and -0.05.Subproblem 1
x + 0.1 = 0.05 Simplifying x + 0.1 = 0.05 Reorder the terms: 0.1 + x = 0.05 Solving 0.1 + x = 0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.05 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.05 + -0.1 x = 0.05 + -0.1 Combine like terms: 0.05 + -0.1 = -0.05 x = -0.05 Simplifying x = -0.05Subproblem 2
x + 0.1 = -0.05 Simplifying x + 0.1 = -0.05 Reorder the terms: 0.1 + x = -0.05 Solving 0.1 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.05 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.05 + -0.1 x = -0.05 + -0.1 Combine like terms: -0.05 + -0.1 = -0.15 x = -0.15 Simplifying x = -0.15Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.05, -0.15}
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