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Simplifying 2474.2x2 + -418.206 + 418.206x = 0 Reorder the terms: -418.206 + 418.206x + 2474.2x2 = 0 Solving -418.206 + 418.206x + 2474.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2474.2 the coefficient of the squared term: Divide each side by '2474.2'. -0.1690267561 + 0.1690267561x + x2 = 0 Move the constant term to the right: Add '0.1690267561' to each side of the equation. -0.1690267561 + 0.1690267561x + 0.1690267561 + x2 = 0 + 0.1690267561 Reorder the terms: -0.1690267561 + 0.1690267561 + 0.1690267561x + x2 = 0 + 0.1690267561 Combine like terms: -0.1690267561 + 0.1690267561 = 0.0000000000 0.0000000000 + 0.1690267561x + x2 = 0 + 0.1690267561 0.1690267561x + x2 = 0 + 0.1690267561 Combine like terms: 0 + 0.1690267561 = 0.1690267561 0.1690267561x + x2 = 0.1690267561 The x term is 0.1690267561x. Take half its coefficient (0.08451337805). Square it (0.007142511069) and add it to both sides. Add '0.007142511069' to each side of the equation. 0.1690267561x + 0.007142511069 + x2 = 0.1690267561 + 0.007142511069 Reorder the terms: 0.007142511069 + 0.1690267561x + x2 = 0.1690267561 + 0.007142511069 Combine like terms: 0.1690267561 + 0.007142511069 = 0.176169267169 0.007142511069 + 0.1690267561x + x2 = 0.176169267169 Factor a perfect square on the left side: (x + 0.08451337805)(x + 0.08451337805) = 0.176169267169 Calculate the square root of the right side: 0.419725228 Break this problem into two subproblems by setting (x + 0.08451337805) equal to 0.419725228 and -0.419725228.Subproblem 1
x + 0.08451337805 = 0.419725228 Simplifying x + 0.08451337805 = 0.419725228 Reorder the terms: 0.08451337805 + x = 0.419725228 Solving 0.08451337805 + x = 0.419725228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08451337805' to each side of the equation. 0.08451337805 + -0.08451337805 + x = 0.419725228 + -0.08451337805 Combine like terms: 0.08451337805 + -0.08451337805 = 0.00000000000 0.00000000000 + x = 0.419725228 + -0.08451337805 x = 0.419725228 + -0.08451337805 Combine like terms: 0.419725228 + -0.08451337805 = 0.33521184995 x = 0.33521184995 Simplifying x = 0.33521184995Subproblem 2
x + 0.08451337805 = -0.419725228 Simplifying x + 0.08451337805 = -0.419725228 Reorder the terms: 0.08451337805 + x = -0.419725228 Solving 0.08451337805 + x = -0.419725228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08451337805' to each side of the equation. 0.08451337805 + -0.08451337805 + x = -0.419725228 + -0.08451337805 Combine like terms: 0.08451337805 + -0.08451337805 = 0.00000000000 0.00000000000 + x = -0.419725228 + -0.08451337805 x = -0.419725228 + -0.08451337805 Combine like terms: -0.419725228 + -0.08451337805 = -0.50423860605 x = -0.50423860605 Simplifying x = -0.50423860605Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.33521184995, -0.50423860605}
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