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Simplifying x2 + 0.0012x + -0.0000000000001 = 0 Reorder the terms: -0.0000000000001 + 0.0012x + x2 = 0 Solving -0.0000000000001 + 0.0012x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0000000000001' to each side of the equation. -0.0000000000001 + 0.0012x + 0.0000000000001 + x2 = 0 + 0.0000000000001 Reorder the terms: -0.0000000000001 + 0.0000000000001 + 0.0012x + x2 = 0 + 0.0000000000001 Combine like terms: -0.0000000000001 + 0.0000000000001 = 0.0000000000000 0.0000000000000 + 0.0012x + x2 = 0 + 0.0000000000001 0.0012x + x2 = 0 + 0.0000000000001 Combine like terms: 0 + 0.0000000000001 = 0.0000000000001 0.0012x + x2 = 0.0000000000001 The x term is 0.0012x. Take half its coefficient (0.0006). Square it (0.00000036) and add it to both sides. Add '0.00000036' to each side of the equation. 0.0012x + 0.00000036 + x2 = 0.0000000000001 + 0.00000036 Reorder the terms: 0.00000036 + 0.0012x + x2 = 0.0000000000001 + 0.00000036 Combine like terms: 0.0000000000001 + 0.00000036 = 0.0000003600001 0.00000036 + 0.0012x + x2 = 0.0000003600001 Factor a perfect square on the left side: (x + 0.0006)(x + 0.0006) = 0.0000003600001 Calculate the square root of the right side: 0.0006 Break this problem into two subproblems by setting (x + 0.0006) equal to 0.0006 and -0.0006.Subproblem 1
x + 0.0006 = 0.0006 Simplifying x + 0.0006 = 0.0006 Reorder the terms: 0.0006 + x = 0.0006 Add '-0.0006' to each side of the equation. 0.0006 + -0.0006 + x = 0.0006 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 0.0000 + x = 0.0006 + -0.0006 x = 0.0006 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 x = 0.0000 Solving x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Simplifying x = 0.0000Subproblem 2
x + 0.0006 = -0.0006 Simplifying x + 0.0006 = -0.0006 Reorder the terms: 0.0006 + x = -0.0006 Solving 0.0006 + x = -0.0006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0006' to each side of the equation. 0.0006 + -0.0006 + x = -0.0006 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 0.0000 + x = -0.0006 + -0.0006 x = -0.0006 + -0.0006 Combine like terms: -0.0006 + -0.0006 = -0.0012 x = -0.0012 Simplifying x = -0.0012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0000, -0.0012}
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