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Simplifying 6x3(6x2 + -8x + 5) = 0 Reorder the terms: 6x3(5 + -8x + 6x2) = 0 (5 * 6x3 + -8x * 6x3 + 6x2 * 6x3) = 0 (30x3 + -48x4 + 36x5) = 0 Solving 30x3 + -48x4 + 36x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x3'. 6x3(5 + -8x + 6x2) = 0 Ignore the factor 6.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 '(5 + -8x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + -8x + 6x2 = 0 Solving 5 + -8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -1.333333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -1.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.8333333333 -1.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -1.333333333x + x2 = -0.8333333333 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 = -0.8333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.8333333333 + 0.4444444442 Combine like terms: -0.8333333333 + 0.4444444442 = -0.3888888891 0.4444444442 + -1.333333333x + x2 = -0.3888888891 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -0.3888888891 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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