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Simplifying X2 + 0.001X + -0.01 = 0 Reorder the terms: -0.01 + 0.001X + X2 = 0 Solving -0.01 + 0.001X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + 0.001X + 0.01 + X2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + 0.001X + X2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + 0.001X + X2 = 0 + 0.01 0.001X + X2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 0.001X + X2 = 0.01 The X term is 0.001X. Take half its coefficient (0.0005). Square it (0.00000025) and add it to both sides. Add '0.00000025' to each side of the equation. 0.001X + 0.00000025 + X2 = 0.01 + 0.00000025 Reorder the terms: 0.00000025 + 0.001X + X2 = 0.01 + 0.00000025 Combine like terms: 0.01 + 0.00000025 = 0.01000025 0.00000025 + 0.001X + X2 = 0.01000025 Factor a perfect square on the left side: (X + 0.0005)(X + 0.0005) = 0.01000025 Calculate the square root of the right side: 0.10000125 Break this problem into two subproblems by setting (X + 0.0005) equal to 0.10000125 and -0.10000125.Subproblem 1
X + 0.0005 = 0.10000125 Simplifying X + 0.0005 = 0.10000125 Reorder the terms: 0.0005 + X = 0.10000125 Solving 0.0005 + X = 0.10000125 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0005' to each side of the equation. 0.0005 + -0.0005 + X = 0.10000125 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = 0.10000125 + -0.0005 X = 0.10000125 + -0.0005 Combine like terms: 0.10000125 + -0.0005 = 0.09950125 X = 0.09950125 Simplifying X = 0.09950125Subproblem 2
X + 0.0005 = -0.10000125 Simplifying X + 0.0005 = -0.10000125 Reorder the terms: 0.0005 + X = -0.10000125 Solving 0.0005 + X = -0.10000125 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.0005' to each side of the equation. 0.0005 + -0.0005 + X = -0.10000125 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = -0.10000125 + -0.0005 X = -0.10000125 + -0.0005 Combine like terms: -0.10000125 + -0.0005 = -0.10050125 X = -0.10050125 Simplifying X = -0.10050125Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.09950125, -0.10050125}
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