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Simplifying (3x2) + (4x) + -399 = 0 Reorder the terms: -399 + (4x) + (3x2) = 0 Solving -399 + (4x) + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -133 + (1.333333333x) + x2 = 0 Move the constant term to the right: Add '133' to each side of the equation. -133 + (1.333333333x) + 133 + x2 = 0 + 133 Reorder the terms: -133 + 133 + (1.333333333x) + x2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + (1.333333333x) + x2 = 0 + 133 (1.333333333x) + x2 = 0 + 133 Combine like terms: 0 + 133 = 133 (1.333333333x) + x2 = 133 The x term is (1.333333333x). Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. (1.333333333x) + 0.4444444442 + x2 = 133 + 0.4444444442 Reorder the terms: 0.4444444442 + (1.333333333x) + x2 = 133 + 0.4444444442 Combine like terms: 133 + 0.4444444442 = 133.4444444442 0.4444444442 + (1.333333333x) + x2 = 133.4444444442 Factor a perfect square on the left side: ((x) + 0.6666666665)((x) + 0.6666666665) = 133.4444444442 Calculate the square root of the right side: 11.551815634 Break this problem into two subproblems by setting ((x) + 0.6666666665) equal to 11.551815634 and -11.551815634.Subproblem 1
(x) + 0.6666666665 = 11.551815634 Simplifying (x) + 0.6666666665 = 11.551815634 x + 0.6666666665 = 11.551815634 Reorder the terms: 0.6666666665 + x = 11.551815634 Solving 0.6666666665 + x = 11.551815634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 11.551815634 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 11.551815634 + -0.6666666665 x = 11.551815634 + -0.6666666665 Combine like terms: 11.551815634 + -0.6666666665 = 10.8851489675 x = 10.8851489675 Simplifying x = 10.8851489675Subproblem 2
(x) + 0.6666666665 = -11.551815634 Simplifying (x) + 0.6666666665 = -11.551815634 x + 0.6666666665 = -11.551815634 Reorder the terms: 0.6666666665 + x = -11.551815634 Solving 0.6666666665 + x = -11.551815634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -11.551815634 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -11.551815634 + -0.6666666665 x = -11.551815634 + -0.6666666665 Combine like terms: -11.551815634 + -0.6666666665 = -12.2184823005 x = -12.2184823005 Simplifying x = -12.2184823005Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.8851489675, -12.2184823005}
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