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Simplifying 6.09x2 + 4.57x + -8.86 = 0 Reorder the terms: -8.86 + 4.57x + 6.09x2 = 0 Solving -8.86 + 4.57x + 6.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.09 the coefficient of the squared term: Divide each side by '6.09'. -1.454844007 + 0.750410509x + x2 = 0 Move the constant term to the right: Add '1.454844007' to each side of the equation. -1.454844007 + 0.750410509x + 1.454844007 + x2 = 0 + 1.454844007 Reorder the terms: -1.454844007 + 1.454844007 + 0.750410509x + x2 = 0 + 1.454844007 Combine like terms: -1.454844007 + 1.454844007 = 0.000000000 0.000000000 + 0.750410509x + x2 = 0 + 1.454844007 0.750410509x + x2 = 0 + 1.454844007 Combine like terms: 0 + 1.454844007 = 1.454844007 0.750410509x + x2 = 1.454844007 The x term is 0.750410509x. Take half its coefficient (0.3752052545). Square it (0.1407789830) and add it to both sides. Add '0.1407789830' to each side of the equation. 0.750410509x + 0.1407789830 + x2 = 1.454844007 + 0.1407789830 Reorder the terms: 0.1407789830 + 0.750410509x + x2 = 1.454844007 + 0.1407789830 Combine like terms: 1.454844007 + 0.1407789830 = 1.59562299 0.1407789830 + 0.750410509x + x2 = 1.59562299 Factor a perfect square on the left side: (x + 0.3752052545)(x + 0.3752052545) = 1.59562299 Calculate the square root of the right side: 1.263179714 Break this problem into two subproblems by setting (x + 0.3752052545) equal to 1.263179714 and -1.263179714.Subproblem 1
x + 0.3752052545 = 1.263179714 Simplifying x + 0.3752052545 = 1.263179714 Reorder the terms: 0.3752052545 + x = 1.263179714 Solving 0.3752052545 + x = 1.263179714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3752052545' to each side of the equation. 0.3752052545 + -0.3752052545 + x = 1.263179714 + -0.3752052545 Combine like terms: 0.3752052545 + -0.3752052545 = 0.0000000000 0.0000000000 + x = 1.263179714 + -0.3752052545 x = 1.263179714 + -0.3752052545 Combine like terms: 1.263179714 + -0.3752052545 = 0.8879744595 x = 0.8879744595 Simplifying x = 0.8879744595Subproblem 2
x + 0.3752052545 = -1.263179714 Simplifying x + 0.3752052545 = -1.263179714 Reorder the terms: 0.3752052545 + x = -1.263179714 Solving 0.3752052545 + x = -1.263179714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3752052545' to each side of the equation. 0.3752052545 + -0.3752052545 + x = -1.263179714 + -0.3752052545 Combine like terms: 0.3752052545 + -0.3752052545 = 0.0000000000 0.0000000000 + x = -1.263179714 + -0.3752052545 x = -1.263179714 + -0.3752052545 Combine like terms: -1.263179714 + -0.3752052545 = -1.6383849685 x = -1.6383849685 Simplifying x = -1.6383849685Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8879744595, -1.6383849685}
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