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Simplifying x2 + 0.05x + (0.00000003) = 0 x2 + 0.05x + 0.00000003 = 0 Reorder the terms: 0.00000003 + 0.05x + x2 = 0 Solving 0.00000003 + 0.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.00000003' to each side of the equation. 0.00000003 + 0.05x + -0.00000003 + x2 = 0 + -0.00000003 Reorder the terms: 0.00000003 + -0.00000003 + 0.05x + x2 = 0 + -0.00000003 Combine like terms: 0.00000003 + -0.00000003 = 0.00000000 0.00000000 + 0.05x + x2 = 0 + -0.00000003 0.05x + x2 = 0 + -0.00000003 Combine like terms: 0 + -0.00000003 = -0.00000003 0.05x + x2 = -0.00000003 The x term is 0.05x. Take half its coefficient (0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. 0.05x + 0.000625 + x2 = -0.00000003 + 0.000625 Reorder the terms: 0.000625 + 0.05x + x2 = -0.00000003 + 0.000625 Combine like terms: -0.00000003 + 0.000625 = 0.00062497 0.000625 + 0.05x + x2 = 0.00062497 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 0.00062497 Calculate the square root of the right side: 0.0249994 Break this problem into two subproblems by setting (x + 0.025) equal to 0.0249994 and -0.0249994.Subproblem 1
x + 0.025 = 0.0249994 Simplifying x + 0.025 = 0.0249994 Reorder the terms: 0.025 + x = 0.0249994 Solving 0.025 + x = 0.0249994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = 0.0249994 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 0.0249994 + -0.025 x = 0.0249994 + -0.025 Combine like terms: 0.0249994 + -0.025 = -0.0000006 x = -0.0000006 Simplifying x = -0.0000006Subproblem 2
x + 0.025 = -0.0249994 Simplifying x + 0.025 = -0.0249994 Reorder the terms: 0.025 + x = -0.0249994 Solving 0.025 + x = -0.0249994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = -0.0249994 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -0.0249994 + -0.025 x = -0.0249994 + -0.025 Combine like terms: -0.0249994 + -0.025 = -0.0499994 x = -0.0499994 Simplifying x = -0.0499994Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0000006, -0.0499994}
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