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Simplifying 12x3 + -56x2 + 120x = 0 Reorder the terms: 120x + -56x2 + 12x3 = 0 Solving 120x + -56x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(30 + -14x + 3x2) = 0 Ignore the factor 4.Subproblem 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 '(30 + -14x + 3x2)' equal to zero and attempt to solve: Simplifying 30 + -14x + 3x2 = 0 Solving 30 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -4.666666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -4.666666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -4.666666667x + x2 = 0 + -10 -4.666666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -4.666666667x + x2 = -10 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -10 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -10 + 5.444444448 Combine like terms: -10 + 5.444444448 = -4.555555552 5.444444448 + -4.666666667x + x2 = -4.555555552 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = -4.555555552 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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