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Simplifying (4x3 + -3x + 2x3) + (2x + -2x2 + 6x) = 0 Reorder the terms: (-3x + 4x3 + 2x3) + (2x + -2x2 + 6x) = 0 Combine like terms: 4x3 + 2x3 = 6x3 (-3x + 6x3) + (2x + -2x2 + 6x) = 0 Remove parenthesis around (-3x + 6x3) -3x + 6x3 + (2x + -2x2 + 6x) = 0 Reorder the terms: -3x + 6x3 + (2x + 6x + -2x2) = 0 Combine like terms: 2x + 6x = 8x -3x + 6x3 + (8x + -2x2) = 0 Remove parenthesis around (8x + -2x2) -3x + 6x3 + 8x + -2x2 = 0 Reorder the terms: -3x + 8x + -2x2 + 6x3 = 0 Combine like terms: -3x + 8x = 5x 5x + -2x2 + 6x3 = 0 Solving 5x + -2x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -2x + 6x2) = 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 '(5 + -2x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + 6x2 = 0 Solving 5 + -2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -0.3333333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -0.3333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + -0.8333333333 -0.3333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -0.3333333333x + x2 = -0.8333333333 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -0.8333333333 + 0.02777777779 Combine like terms: -0.8333333333 + 0.02777777779 = -0.80555555551 0.02777777779 + -0.3333333333x + x2 = -0.80555555551 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.80555555551 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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