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Simplifying -6x5 + 6x4 + -2x3 = 0 Reorder the terms: -2x3 + 6x4 + -6x5 = 0 Solving -2x3 + 6x4 + -6x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(-1 + 3x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + 3x + -3x2)' equal to zero and attempt to solve: Simplifying -1 + 3x + -3x2 = 0 Solving -1 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.3333333333 -1x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1x + x2 = -0.3333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + -1x + x2 = -0.0833333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.0833333333 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. The solution to this equation could not be determined.
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