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Simplifying (0.00000001 + x) * x = 0.00000000000001 Reorder the terms for easier multiplication: x(0.00000001 + x) = 0.00000000000001 (0.00000001 * x + x * x) = 0.00000000000001 (0.00000001x + x2) = 0.00000000000001 Solving 0.00000001x + x2 = 0.00000000000001 Solving for variable 'x'. Reorder the terms: -0.00000000000001 + 0.00000001x + x2 = 0.00000000000001 + -0.00000000000001 Combine like terms: 0.00000000000001 + -0.00000000000001 = 0.00000000000000 -0.00000000000001 + 0.00000001x + x2 = 0.00000000000000 Begin completing the square. Move the constant term to the right: Add '0.00000000000001' to each side of the equation. -0.00000000000001 + 0.00000001x + 0.00000000000001 + x2 = 0.00000000000000 + 0.00000000000001 Reorder the terms: -0.00000000000001 + 0.00000000000001 + 0.00000001x + x2 = 0.00000000000000 + 0.00000000000001 Combine like terms: -0.00000000000001 + 0.00000000000001 = 0.00000000000000 0.00000000000000 + 0.00000001x + x2 = 0.00000000000000 + 0.00000000000001 0.00000001x + x2 = 0.00000000000000 + 0.00000000000001 Combine like terms: 0.00000000000000 + 0.00000000000001 = 0.00000000000001 0.00000001x + x2 = 0.00000000000001 The x term is 0.00000001x. Take half its coefficient (0.000000005). Square it (0.000000000000000025) and add it to both sides. Add '0.000000000000000025' to each side of the equation. 0.00000001x + 0.000000000000000025 + x2 = 0.00000000000001 + 0.000000000000000025 Reorder the terms: 0.000000000000000025 + 0.00000001x + x2 = 0.00000000000001 + 0.000000000000000025 Combine like terms: 0.00000000000001 + 0.000000000000000025 = 0.000000000000010025 0.000000000000000025 + 0.00000001x + x2 = 0.000000000000010025 Factor a perfect square on the left side: (x + 0.000000005)(x + 0.000000005) = 0.000000000000010025 Calculate the square root of the right side: 0.0000001 Break this problem into two subproblems by setting (x + 0.000000005) equal to 0.0000001 and -0.0000001.Subproblem 1
x + 0.000000005 = 0.0000001 Simplifying x + 0.000000005 = 0.0000001 Reorder the terms: 0.000000005 + x = 0.0000001 Solving 0.000000005 + x = 0.0000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000005' to each side of the equation. 0.000000005 + -0.000000005 + x = 0.0000001 + -0.000000005 Combine like terms: 0.000000005 + -0.000000005 = 0.000000000 0.000000000 + x = 0.0000001 + -0.000000005 x = 0.0000001 + -0.000000005 Combine like terms: 0.0000001 + -0.000000005 = 0.000000095 x = 0.000000095 Simplifying x = 0.000000095Subproblem 2
x + 0.000000005 = -0.0000001 Simplifying x + 0.000000005 = -0.0000001 Reorder the terms: 0.000000005 + x = -0.0000001 Solving 0.000000005 + x = -0.0000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000000005' to each side of the equation. 0.000000005 + -0.000000005 + x = -0.0000001 + -0.000000005 Combine like terms: 0.000000005 + -0.000000005 = 0.000000000 0.000000000 + x = -0.0000001 + -0.000000005 x = -0.0000001 + -0.000000005 Combine like terms: -0.0000001 + -0.000000005 = -0.000000105 x = -0.000000105 Simplifying x = -0.000000105Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000000095, -0.000000105}
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