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Simplifying 3x2 + -4x = 96 Reorder the terms: -4x + 3x2 = 96 Solving -4x + 3x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + -4x + 3x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -4x + 3x2 = 0 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 = 6.3626691635 x = 6.3626691635 Simplifying x = 6.3626691635Subproblem 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 = -5.0293358305 x = -5.0293358305 Simplifying x = -5.0293358305Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.3626691635, -5.0293358305}
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