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Simplifying x2 + 0.000064x + -0.0000128 = 0 Reorder the terms: -0.0000128 + 0.000064x + x2 = 0 Solving -0.0000128 + 0.000064x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0000128' to each side of the equation. -0.0000128 + 0.000064x + 0.0000128 + x2 = 0 + 0.0000128 Reorder the terms: -0.0000128 + 0.0000128 + 0.000064x + x2 = 0 + 0.0000128 Combine like terms: -0.0000128 + 0.0000128 = 0.0000000 0.0000000 + 0.000064x + x2 = 0 + 0.0000128 0.000064x + x2 = 0 + 0.0000128 Combine like terms: 0 + 0.0000128 = 0.0000128 0.000064x + x2 = 0.0000128 The x term is 0.000064x. Take half its coefficient (0.000032). Square it (0.000000001024) and add it to both sides. Add '0.000000001024' to each side of the equation. 0.000064x + 0.000000001024 + x2 = 0.0000128 + 0.000000001024 Reorder the terms: 0.000000001024 + 0.000064x + x2 = 0.0000128 + 0.000000001024 Combine like terms: 0.0000128 + 0.000000001024 = 0.000012801024 0.000000001024 + 0.000064x + x2 = 0.000012801024 Factor a perfect square on the left side: (x + 0.000032)(x + 0.000032) = 0.000012801024 Calculate the square root of the right side: 0.003577852 Break this problem into two subproblems by setting (x + 0.000032) equal to 0.003577852 and -0.003577852.Subproblem 1
x + 0.000032 = 0.003577852 Simplifying x + 0.000032 = 0.003577852 Reorder the terms: 0.000032 + x = 0.003577852 Solving 0.000032 + x = 0.003577852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000032' to each side of the equation. 0.000032 + -0.000032 + x = 0.003577852 + -0.000032 Combine like terms: 0.000032 + -0.000032 = 0.000000 0.000000 + x = 0.003577852 + -0.000032 x = 0.003577852 + -0.000032 Combine like terms: 0.003577852 + -0.000032 = 0.003545852 x = 0.003545852 Simplifying x = 0.003545852Subproblem 2
x + 0.000032 = -0.003577852 Simplifying x + 0.000032 = -0.003577852 Reorder the terms: 0.000032 + x = -0.003577852 Solving 0.000032 + x = -0.003577852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000032' to each side of the equation. 0.000032 + -0.000032 + x = -0.003577852 + -0.000032 Combine like terms: 0.000032 + -0.000032 = 0.000000 0.000000 + x = -0.003577852 + -0.000032 x = -0.003577852 + -0.000032 Combine like terms: -0.003577852 + -0.000032 = -0.003609852 x = -0.003609852 Simplifying x = -0.003609852Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.003545852, -0.003609852}
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