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Simplifying x2 + 0.004x + -0.000457 = 0 Reorder the terms: -0.000457 + 0.004x + x2 = 0 Solving -0.000457 + 0.004x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000457' to each side of the equation. -0.000457 + 0.004x + 0.000457 + x2 = 0 + 0.000457 Reorder the terms: -0.000457 + 0.000457 + 0.004x + x2 = 0 + 0.000457 Combine like terms: -0.000457 + 0.000457 = 0.000000 0.000000 + 0.004x + x2 = 0 + 0.000457 0.004x + x2 = 0 + 0.000457 Combine like terms: 0 + 0.000457 = 0.000457 0.004x + x2 = 0.000457 The x term is 0.004x. Take half its coefficient (0.002). Square it (0.000004) and add it to both sides. Add '0.000004' to each side of the equation. 0.004x + 0.000004 + x2 = 0.000457 + 0.000004 Reorder the terms: 0.000004 + 0.004x + x2 = 0.000457 + 0.000004 Combine like terms: 0.000457 + 0.000004 = 0.000461 0.000004 + 0.004x + x2 = 0.000461 Factor a perfect square on the left side: (x + 0.002)(x + 0.002) = 0.000461 Calculate the square root of the right side: 0.021470911 Break this problem into two subproblems by setting (x + 0.002) equal to 0.021470911 and -0.021470911.Subproblem 1
x + 0.002 = 0.021470911 Simplifying x + 0.002 = 0.021470911 Reorder the terms: 0.002 + x = 0.021470911 Solving 0.002 + x = 0.021470911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.002' to each side of the equation. 0.002 + -0.002 + x = 0.021470911 + -0.002 Combine like terms: 0.002 + -0.002 = 0.000 0.000 + x = 0.021470911 + -0.002 x = 0.021470911 + -0.002 Combine like terms: 0.021470911 + -0.002 = 0.019470911 x = 0.019470911 Simplifying x = 0.019470911Subproblem 2
x + 0.002 = -0.021470911 Simplifying x + 0.002 = -0.021470911 Reorder the terms: 0.002 + x = -0.021470911 Solving 0.002 + x = -0.021470911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.002' to each side of the equation. 0.002 + -0.002 + x = -0.021470911 + -0.002 Combine like terms: 0.002 + -0.002 = 0.000 0.000 + x = -0.021470911 + -0.002 x = -0.021470911 + -0.002 Combine like terms: -0.021470911 + -0.002 = -0.023470911 x = -0.023470911 Simplifying x = -0.023470911Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019470911, -0.023470911}
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