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Simplifying x2 + 0.005x + -0.001 = 0 Reorder the terms: -0.001 + 0.005x + x2 = 0 Solving -0.001 + 0.005x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.001' to each side of the equation. -0.001 + 0.005x + 0.001 + x2 = 0 + 0.001 Reorder the terms: -0.001 + 0.001 + 0.005x + x2 = 0 + 0.001 Combine like terms: -0.001 + 0.001 = 0.000 0.000 + 0.005x + x2 = 0 + 0.001 0.005x + x2 = 0 + 0.001 Combine like terms: 0 + 0.001 = 0.001 0.005x + x2 = 0.001 The x term is 0.005x. Take half its coefficient (0.0025). Square it (0.00000625) and add it to both sides. Add '0.00000625' to each side of the equation. 0.005x + 0.00000625 + x2 = 0.001 + 0.00000625 Reorder the terms: 0.00000625 + 0.005x + x2 = 0.001 + 0.00000625 Combine like terms: 0.001 + 0.00000625 = 0.00100625 0.00000625 + 0.005x + x2 = 0.00100625 Factor a perfect square on the left side: (x + 0.0025)(x + 0.0025) = 0.00100625 Calculate the square root of the right side: 0.031721444 Break this problem into two subproblems by setting (x + 0.0025) equal to 0.031721444 and -0.031721444.Subproblem 1
x + 0.0025 = 0.031721444 Simplifying x + 0.0025 = 0.031721444 Reorder the terms: 0.0025 + x = 0.031721444 Solving 0.0025 + x = 0.031721444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0025' to each side of the equation. 0.0025 + -0.0025 + x = 0.031721444 + -0.0025 Combine like terms: 0.0025 + -0.0025 = 0.0000 0.0000 + x = 0.031721444 + -0.0025 x = 0.031721444 + -0.0025 Combine like terms: 0.031721444 + -0.0025 = 0.029221444 x = 0.029221444 Simplifying x = 0.029221444Subproblem 2
x + 0.0025 = -0.031721444 Simplifying x + 0.0025 = -0.031721444 Reorder the terms: 0.0025 + x = -0.031721444 Solving 0.0025 + x = -0.031721444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0025' to each side of the equation. 0.0025 + -0.0025 + x = -0.031721444 + -0.0025 Combine like terms: 0.0025 + -0.0025 = 0.0000 0.0000 + x = -0.031721444 + -0.0025 x = -0.031721444 + -0.0025 Combine like terms: -0.031721444 + -0.0025 = -0.034221444 x = -0.034221444 Simplifying x = -0.034221444Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.029221444, -0.034221444}
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