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Simplifying (0.050 + x)(0.040 + x) = 0 Multiply (0.050 + x) * (0.040 + x) (0.050(0.040 + x) + x(0.040 + x)) = 0 ((0.040 * 0.050 + x * 0.050) + x(0.040 + x)) = 0 ((0.002 + 0.050x) + x(0.040 + x)) = 0 (0.002 + 0.050x + (0.040 * x + x * x)) = 0 (0.002 + 0.050x + (0.040x + x2)) = 0 Combine like terms: 0.050x + 0.040x = 0.09x (0.002 + 0.09x + x2) = 0 Solving 0.002 + 0.09x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.002' to each side of the equation. 0.002 + 0.09x + -0.002 + x2 = 0 + -0.002 Reorder the terms: 0.002 + -0.002 + 0.09x + x2 = 0 + -0.002 Combine like terms: 0.002 + -0.002 = 0.000 0.000 + 0.09x + x2 = 0 + -0.002 0.09x + x2 = 0 + -0.002 Combine like terms: 0 + -0.002 = -0.002 0.09x + x2 = -0.002 The x term is 0.09x. Take half its coefficient (0.045). Square it (0.002025) and add it to both sides. Add '0.002025' to each side of the equation. 0.09x + 0.002025 + x2 = -0.002 + 0.002025 Reorder the terms: 0.002025 + 0.09x + x2 = -0.002 + 0.002025 Combine like terms: -0.002 + 0.002025 = 0.000025 0.002025 + 0.09x + x2 = 0.000025 Factor a perfect square on the left side: (x + 0.045)(x + 0.045) = 0.000025 Calculate the square root of the right side: 0.005 Break this problem into two subproblems by setting (x + 0.045) equal to 0.005 and -0.005.Subproblem 1
x + 0.045 = 0.005 Simplifying x + 0.045 = 0.005 Reorder the terms: 0.045 + x = 0.005 Solving 0.045 + x = 0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.045' to each side of the equation. 0.045 + -0.045 + x = 0.005 + -0.045 Combine like terms: 0.045 + -0.045 = 0.000 0.000 + x = 0.005 + -0.045 x = 0.005 + -0.045 Combine like terms: 0.005 + -0.045 = -0.04 x = -0.04 Simplifying x = -0.04Subproblem 2
x + 0.045 = -0.005 Simplifying x + 0.045 = -0.005 Reorder the terms: 0.045 + x = -0.005 Solving 0.045 + x = -0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.045' to each side of the equation. 0.045 + -0.045 + x = -0.005 + -0.045 Combine like terms: 0.045 + -0.045 = 0.000 0.000 + x = -0.005 + -0.045 x = -0.005 + -0.045 Combine like terms: -0.005 + -0.045 = -0.05 x = -0.05 Simplifying x = -0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.04, -0.05}
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