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Simplifying X2 + 0.001X + -0.003 = 0 Reorder the terms: -0.003 + 0.001X + X2 = 0 Solving -0.003 + 0.001X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.003' to each side of the equation. -0.003 + 0.001X + 0.003 + X2 = 0 + 0.003 Reorder the terms: -0.003 + 0.003 + 0.001X + X2 = 0 + 0.003 Combine like terms: -0.003 + 0.003 = 0.000 0.000 + 0.001X + X2 = 0 + 0.003 0.001X + X2 = 0 + 0.003 Combine like terms: 0 + 0.003 = 0.003 0.001X + X2 = 0.003 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 = 0.003 + 0.00000025 Reorder the terms: 0.00000025 + 0.001X + X2 = 0.003 + 0.00000025 Combine like terms: 0.003 + 0.00000025 = 0.00300025 0.00000025 + 0.001X + X2 = 0.00300025 Factor a perfect square on the left side: (X + 0.0005)(X + 0.0005) = 0.00300025 Calculate the square root of the right side: 0.054774538 Break this problem into two subproblems by setting (X + 0.0005) equal to 0.054774538 and -0.054774538.Subproblem 1
X + 0.0005 = 0.054774538 Simplifying X + 0.0005 = 0.054774538 Reorder the terms: 0.0005 + X = 0.054774538 Solving 0.0005 + X = 0.054774538 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 = 0.054774538 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = 0.054774538 + -0.0005 X = 0.054774538 + -0.0005 Combine like terms: 0.054774538 + -0.0005 = 0.054274538 X = 0.054274538 Simplifying X = 0.054274538Subproblem 2
X + 0.0005 = -0.054774538 Simplifying X + 0.0005 = -0.054774538 Reorder the terms: 0.0005 + X = -0.054774538 Solving 0.0005 + X = -0.054774538 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 = -0.054774538 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = -0.054774538 + -0.0005 X = -0.054774538 + -0.0005 Combine like terms: -0.054774538 + -0.0005 = -0.055274538 X = -0.055274538 Simplifying X = -0.055274538Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.054274538, -0.055274538}
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