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Simplifying 3x3 + -4x2 + 192x = 0 Reorder the terms: 192x + -4x2 + 3x3 = 0 Solving 192x + -4x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(192 + -4x + 3x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(192 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 192 + -4x + 3x2 = 0 Solving 192 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 64 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -1.333333333x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -1.333333333x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -1.333333333x + x2 = 0 + -64 -1.333333333x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -1.333333333x + x2 = -64 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 = -64 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -64 + 0.4444444442 Combine like terms: -64 + 0.4444444442 = -63.5555555558 0.4444444442 + -1.333333333x + x2 = -63.5555555558 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -63.5555555558 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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