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Simplifying (x2) + (0.000018) * x + -1(0.000018) = 0 x2 + (0.000018) * x + -1(0.000018) = 0 Multiply -1 * 0.000018 x2 + 0.000018x + -0.000018 = 0 Reorder the terms: -0.000018 + 0.000018x + x2 = 0 Solving -0.000018 + 0.000018x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000018' to each side of the equation. -0.000018 + 0.000018x + 0.000018 + x2 = 0 + 0.000018 Reorder the terms: -0.000018 + 0.000018 + 0.000018x + x2 = 0 + 0.000018 Combine like terms: -0.000018 + 0.000018 = 0.000000 0.000000 + 0.000018x + x2 = 0 + 0.000018 0.000018x + x2 = 0 + 0.000018 Combine like terms: 0 + 0.000018 = 0.000018 0.000018x + x2 = 0.000018 The x term is 0.000018x. Take half its coefficient (0.000009). Square it (0.000000000081) and add it to both sides. Add '0.000000000081' to each side of the equation. 0.000018x + 0.000000000081 + x2 = 0.000018 + 0.000000000081 Reorder the terms: 0.000000000081 + 0.000018x + x2 = 0.000018 + 0.000000000081 Combine like terms: 0.000018 + 0.000000000081 = 0.000018000081 0.000000000081 + 0.000018x + x2 = 0.000018000081 Factor a perfect square on the left side: (x + 0.000009)(x + 0.000009) = 0.000018000081 Calculate the square root of the right side: 0.00424265 Break this problem into two subproblems by setting (x + 0.000009) equal to 0.00424265 and -0.00424265.Subproblem 1
x + 0.000009 = 0.00424265 Simplifying x + 0.000009 = 0.00424265 Reorder the terms: 0.000009 + x = 0.00424265 Solving 0.000009 + x = 0.00424265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = 0.00424265 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = 0.00424265 + -0.000009 x = 0.00424265 + -0.000009 Combine like terms: 0.00424265 + -0.000009 = 0.00423365 x = 0.00423365 Simplifying x = 0.00423365Subproblem 2
x + 0.000009 = -0.00424265 Simplifying x + 0.000009 = -0.00424265 Reorder the terms: 0.000009 + x = -0.00424265 Solving 0.000009 + x = -0.00424265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000009' to each side of the equation. 0.000009 + -0.000009 + x = -0.00424265 + -0.000009 Combine like terms: 0.000009 + -0.000009 = 0.000000 0.000000 + x = -0.00424265 + -0.000009 x = -0.00424265 + -0.000009 Combine like terms: -0.00424265 + -0.000009 = -0.00425165 x = -0.00425165 Simplifying x = -0.00425165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00423365, -0.00425165}
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