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Simplifying 3x2 + 4x + -96 = 0 Reorder the terms: -96 + 4x + 3x2 = 0 Solving -96 + 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'. -32 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 1.333333333x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 1.333333333x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 1.333333333x + x2 = 0 + 32 1.333333333x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 1.333333333x + x2 = 32 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 = 32 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 32 + 0.4444444442 Combine like terms: 32 + 0.4444444442 = 32.4444444442 0.4444444442 + 1.333333333x + x2 = 32.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 32.4444444442 Calculate the square root of the right side: 5.696002497 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 5.696002497 and -5.696002497.Subproblem 1
x + 0.6666666665 = 5.696002497 Simplifying x + 0.6666666665 = 5.696002497 Reorder the terms: 0.6666666665 + x = 5.696002497 Solving 0.6666666665 + x = 5.696002497 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 = 5.696002497 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 5.696002497 + -0.6666666665 x = 5.696002497 + -0.6666666665 Combine like terms: 5.696002497 + -0.6666666665 = 5.0293358305 x = 5.0293358305 Simplifying x = 5.0293358305Subproblem 2
x + 0.6666666665 = -5.696002497 Simplifying x + 0.6666666665 = -5.696002497 Reorder the terms: 0.6666666665 + x = -5.696002497 Solving 0.6666666665 + x = -5.696002497 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 = -5.696002497 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -5.696002497 + -0.6666666665 x = -5.696002497 + -0.6666666665 Combine like terms: -5.696002497 + -0.6666666665 = -6.3626691635 x = -6.3626691635 Simplifying x = -6.3626691635Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.0293358305, -6.3626691635}
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