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Simplifying 2x2 + 0.00000942x + -0.00005087 = 0 Reorder the terms: -0.00005087 + 0.00000942x + 2x2 = 0 Solving -0.00005087 + 0.00000942x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.000025435 + 0.00000471x + x2 = 0 Move the constant term to the right: Add '0.000025435' to each side of the equation. -0.000025435 + 0.00000471x + 0.000025435 + x2 = 0 + 0.000025435 Reorder the terms: -0.000025435 + 0.000025435 + 0.00000471x + x2 = 0 + 0.000025435 Combine like terms: -0.000025435 + 0.000025435 = 0.000000000 0.000000000 + 0.00000471x + x2 = 0 + 0.000025435 0.00000471x + x2 = 0 + 0.000025435 Combine like terms: 0 + 0.000025435 = 0.000025435 0.00000471x + x2 = 0.000025435 The x term is 0.00000471x. Take half its coefficient (0.000002355). Square it (0.000000000005546025) and add it to both sides. Add '0.000000000005546025' to each side of the equation. 0.00000471x + 0.000000000005546025 + x2 = 0.000025435 + 0.000000000005546025 Reorder the terms: 0.000000000005546025 + 0.00000471x + x2 = 0.000025435 + 0.000000000005546025 Combine like terms: 0.000025435 + 0.000000000005546025 = 0.000025435005546025 0.000000000005546025 + 0.00000471x + x2 = 0.000025435005546025 Factor a perfect square on the left side: (x + 0.000002355)(x + 0.000002355) = 0.000025435005546025 Calculate the square root of the right side: 0.005043313 Break this problem into two subproblems by setting (x + 0.000002355) equal to 0.005043313 and -0.005043313.Subproblem 1
x + 0.000002355 = 0.005043313 Simplifying x + 0.000002355 = 0.005043313 Reorder the terms: 0.000002355 + x = 0.005043313 Solving 0.000002355 + x = 0.005043313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000002355' to each side of the equation. 0.000002355 + -0.000002355 + x = 0.005043313 + -0.000002355 Combine like terms: 0.000002355 + -0.000002355 = 0.000000000 0.000000000 + x = 0.005043313 + -0.000002355 x = 0.005043313 + -0.000002355 Combine like terms: 0.005043313 + -0.000002355 = 0.005040958 x = 0.005040958 Simplifying x = 0.005040958Subproblem 2
x + 0.000002355 = -0.005043313 Simplifying x + 0.000002355 = -0.005043313 Reorder the terms: 0.000002355 + x = -0.005043313 Solving 0.000002355 + x = -0.005043313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000002355' to each side of the equation. 0.000002355 + -0.000002355 + x = -0.005043313 + -0.000002355 Combine like terms: 0.000002355 + -0.000002355 = 0.000000000 0.000000000 + x = -0.005043313 + -0.000002355 x = -0.005043313 + -0.000002355 Combine like terms: -0.005043313 + -0.000002355 = -0.005045668 x = -0.005045668 Simplifying x = -0.005045668Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005040958, -0.005045668}
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