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Simplifying 8x3 = 8x2 + -6x Reorder the terms: 8x3 = -6x + 8x2 Solving 8x3 = -6x + 8x2 Solving for variable 'x'. Reorder the terms: 6x + -8x2 + 8x3 = -6x + 8x2 + 6x + -8x2 Reorder the terms: 6x + -8x2 + 8x3 = -6x + 6x + 8x2 + -8x2 Combine like terms: -6x + 6x = 0 6x + -8x2 + 8x3 = 0 + 8x2 + -8x2 6x + -8x2 + 8x3 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 6x + -8x2 + 8x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -4x + 4x2) = 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 '(3 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 4x2 = 0 Solving 3 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -1x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1x + x2 = 0 + -0.75 -1x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1x + x2 = -0.75 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 = -0.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + -1x + x2 = -0.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.5 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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