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Simplifying X2 + 0.00000000001X + -0.00000000004 = 0 Reorder the terms: -0.00000000004 + 0.00000000001X + X2 = 0 Solving -0.00000000004 + 0.00000000001X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '0.00000000004' to each side of the equation. -0.00000000004 + 0.00000000001X + 0.00000000004 + X2 = 0 + 0.00000000004 Reorder the terms: -0.00000000004 + 0.00000000004 + 0.00000000001X + X2 = 0 + 0.00000000004 Combine like terms: -0.00000000004 + 0.00000000004 = 0.00000000000 0.00000000000 + 0.00000000001X + X2 = 0 + 0.00000000004 0.00000000001X + X2 = 0 + 0.00000000004 Combine like terms: 0 + 0.00000000004 = 0.00000000004 0.00000000001X + X2 = 0.00000000004 The X term is 0.00000000001X. Take half its coefficient (0.000000000005). Square it (0.000000000000000000000025) and add it to both sides. Add '0.000000000000000000000025' to each side of the equation. 0.00000000001X + 0.000000000000000000000025 + X2 = 0.00000000004 + 0.000000000000000000000025 Reorder the terms: 0.000000000000000000000025 + 0.00000000001X + X2 = 0.00000000004 + 0.000000000000000000000025 Combine like terms: 0.00000000004 + 0.000000000000000000000025 = 0.000000000040000000000025 0.000000000000000000000025 + 0.00000000001X + X2 = 0.000000000040000000000025 Factor a perfect square on the left side: (X + 0.000000000005)(X + 0.000000000005) = 0.000000000040000000000025 Calculate the square root of the right side: 0.000006325 Break this problem into two subproblems by setting (X + 0.000000000005) equal to 0.000006325 and -0.000006325.Subproblem 1
X + 0.000000000005 = 0.000006325 Simplifying X + 0.000000000005 = 0.000006325 Reorder the terms: 0.000000000005 + X = 0.000006325 Solving 0.000000000005 + X = 0.000006325 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.000000000005' to each side of the equation. 0.000000000005 + -0.000000000005 + X = 0.000006325 + -0.000000000005 Combine like terms: 0.000000000005 + -0.000000000005 = 0.000000000000 0.000000000000 + X = 0.000006325 + -0.000000000005 X = 0.000006325 + -0.000000000005 Combine like terms: 0.000006325 + -0.000000000005 = 0.000006324995 X = 0.000006324995 Simplifying X = 0.000006324995Subproblem 2
X + 0.000000000005 = -0.000006325 Simplifying X + 0.000000000005 = -0.000006325 Reorder the terms: 0.000000000005 + X = -0.000006325 Solving 0.000000000005 + X = -0.000006325 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.000000000005' to each side of the equation. 0.000000000005 + -0.000000000005 + X = -0.000006325 + -0.000000000005 Combine like terms: 0.000000000005 + -0.000000000005 = 0.000000000000 0.000000000000 + X = -0.000006325 + -0.000000000005 X = -0.000006325 + -0.000000000005 Combine like terms: -0.000006325 + -0.000000000005 = -0.000006325005 X = -0.000006325005 Simplifying X = -0.000006325005Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.000006324995, -0.000006325005}
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