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Simplifying 6x + 4 + -4(4 + -4x + 2x2) * x = 2x3 + 4x2 + 2x + 4 Reorder the terms for easier multiplication: 6x + 4 + -4x(4 + -4x + 2x2) = 2x3 + 4x2 + 2x + 4 6x + 4 + (4 * -4x + -4x * -4x + 2x2 * -4x) = 2x3 + 4x2 + 2x + 4 6x + 4 + (-16x + 16x2 + -8x3) = 2x3 + 4x2 + 2x + 4 Reorder the terms: 4 + 6x + -16x + 16x2 + -8x3 = 2x3 + 4x2 + 2x + 4 Combine like terms: 6x + -16x = -10x 4 + -10x + 16x2 + -8x3 = 2x3 + 4x2 + 2x + 4 Reorder the terms: 4 + -10x + 16x2 + -8x3 = 4 + 2x + 4x2 + 2x3 Add '-4' to each side of the equation. 4 + -10x + 16x2 + -4 + -8x3 = 4 + 2x + 4x2 + -4 + 2x3 Reorder the terms: 4 + -4 + -10x + 16x2 + -8x3 = 4 + 2x + 4x2 + -4 + 2x3 Combine like terms: 4 + -4 = 0 0 + -10x + 16x2 + -8x3 = 4 + 2x + 4x2 + -4 + 2x3 -10x + 16x2 + -8x3 = 4 + 2x + 4x2 + -4 + 2x3 Reorder the terms: -10x + 16x2 + -8x3 = 4 + -4 + 2x + 4x2 + 2x3 Combine like terms: 4 + -4 = 0 -10x + 16x2 + -8x3 = 0 + 2x + 4x2 + 2x3 -10x + 16x2 + -8x3 = 2x + 4x2 + 2x3 Solving -10x + 16x2 + -8x3 = 2x + 4x2 + 2x3 Solving for variable 'x'. Reorder the terms: -10x + -2x + 16x2 + -4x2 + -8x3 + -2x3 = 2x + 4x2 + 2x3 + -2x + -4x2 + -2x3 Combine like terms: -10x + -2x = -12x -12x + 16x2 + -4x2 + -8x3 + -2x3 = 2x + 4x2 + 2x3 + -2x + -4x2 + -2x3 Combine like terms: 16x2 + -4x2 = 12x2 -12x + 12x2 + -8x3 + -2x3 = 2x + 4x2 + 2x3 + -2x + -4x2 + -2x3 Combine like terms: -8x3 + -2x3 = -10x3 -12x + 12x2 + -10x3 = 2x + 4x2 + 2x3 + -2x + -4x2 + -2x3 Reorder the terms: -12x + 12x2 + -10x3 = 2x + -2x + 4x2 + -4x2 + 2x3 + -2x3 Combine like terms: 2x + -2x = 0 -12x + 12x2 + -10x3 = 0 + 4x2 + -4x2 + 2x3 + -2x3 -12x + 12x2 + -10x3 = 4x2 + -4x2 + 2x3 + -2x3 Combine like terms: 4x2 + -4x2 = 0 -12x + 12x2 + -10x3 = 0 + 2x3 + -2x3 -12x + 12x2 + -10x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -12x + 12x2 + -10x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-6 + 6x + -5x2) = 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 '(-6 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -6 + 6x + -5x2 = 0 Solving -6 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.2 + -1.2x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -1.2x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -1.2x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -1.2x + x2 = 0 + -1.2 -1.2x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -1.2x + x2 = -1.2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -1.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -1.2 + 0.36 Combine like terms: -1.2 + 0.36 = -0.84 0.36 + -1.2x + x2 = -0.84 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -0.84 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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