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Simplifying X2 + 0.001X + -0.004 = 0 Reorder the terms: -0.004 + 0.001X + X2 = 0 Solving -0.004 + 0.001X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.004' to each side of the equation. -0.004 + 0.001X + 0.004 + X2 = 0 + 0.004 Reorder the terms: -0.004 + 0.004 + 0.001X + X2 = 0 + 0.004 Combine like terms: -0.004 + 0.004 = 0.000 0.000 + 0.001X + X2 = 0 + 0.004 0.001X + X2 = 0 + 0.004 Combine like terms: 0 + 0.004 = 0.004 0.001X + X2 = 0.004 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 = 0.004 + 0.00000025 Reorder the terms: 0.00000025 + 0.001X + X2 = 0.004 + 0.00000025 Combine like terms: 0.004 + 0.00000025 = 0.00400025 0.00000025 + 0.001X + X2 = 0.00400025 Factor a perfect square on the left side: (X + 0.0005)(X + 0.0005) = 0.00400025 Calculate the square root of the right side: 0.06324753 Break this problem into two subproblems by setting (X + 0.0005) equal to 0.06324753 and -0.06324753.Subproblem 1
X + 0.0005 = 0.06324753 Simplifying X + 0.0005 = 0.06324753 Reorder the terms: 0.0005 + X = 0.06324753 Solving 0.0005 + X = 0.06324753 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 = 0.06324753 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = 0.06324753 + -0.0005 X = 0.06324753 + -0.0005 Combine like terms: 0.06324753 + -0.0005 = 0.06274753 X = 0.06274753 Simplifying X = 0.06274753Subproblem 2
X + 0.0005 = -0.06324753 Simplifying X + 0.0005 = -0.06324753 Reorder the terms: 0.0005 + X = -0.06324753 Solving 0.0005 + X = -0.06324753 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 = -0.06324753 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = -0.06324753 + -0.0005 X = -0.06324753 + -0.0005 Combine like terms: -0.06324753 + -0.0005 = -0.06374753 X = -0.06374753 Simplifying X = -0.06374753Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.06274753, -0.06374753}
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