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Simplifying 24x3 + -6x2 + 8x = 0 Reorder the terms: 8x + -6x2 + 24x3 = 0 Solving 8x + -6x2 + 24x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(4 + -3x + 12x2) = 0 Ignore the factor 2.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 '(4 + -3x + 12x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + 12x2 = 0 Solving 4 + -3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + -0.25x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.25x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.25x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + -0.3333333333 -0.25x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.25x + x2 = -0.3333333333 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -0.3333333333 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -0.3333333333 + 0.015625 Combine like terms: -0.3333333333 + 0.015625 = -0.3177083333 0.015625 + -0.25x + x2 = -0.3177083333 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = -0.3177083333 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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