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Simplifying -12x3 + 8x2 + -120x = 0 Reorder the terms: -120x + 8x2 + -12x3 = 0 Solving -120x + 8x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-30 + 2x + -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 + 2x + -3x2)' equal to zero and attempt to solve: Simplifying -30 + 2x + -3x2 = 0 Solving -30 + 2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -0.6666666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -0.6666666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -0.6666666667x + x2 = 0 + -10 -0.6666666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -0.6666666667x + x2 = -10 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -10 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -10 + 0.1111111112 Combine like terms: -10 + 0.1111111112 = -9.8888888888 0.1111111112 + -0.6666666667x + x2 = -9.8888888888 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -9.8888888888 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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