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Simplifying (5x2 + -4x + 16) + -1(3x3 + 2x2 + 16) = 0 Reorder the terms: (16 + -4x + 5x2) + -1(3x3 + 2x2 + 16) = 0 Remove parenthesis around (16 + -4x + 5x2) 16 + -4x + 5x2 + -1(3x3 + 2x2 + 16) = 0 Reorder the terms: 16 + -4x + 5x2 + -1(16 + 2x2 + 3x3) = 0 16 + -4x + 5x2 + (16 * -1 + 2x2 * -1 + 3x3 * -1) = 0 16 + -4x + 5x2 + (-16 + -2x2 + -3x3) = 0 Reorder the terms: 16 + -16 + -4x + 5x2 + -2x2 + -3x3 = 0 Combine like terms: 16 + -16 = 0 0 + -4x + 5x2 + -2x2 + -3x3 = 0 -4x + 5x2 + -2x2 + -3x3 = 0 Combine like terms: 5x2 + -2x2 = 3x2 -4x + 3x2 + -3x3 = 0 Solving -4x + 3x2 + -3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 3x + -3x2) = 0Subproblem 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 + -3x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + -3x2 = 0 Solving -4 + 3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + -1.333333333 -1x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1x + x2 = -1.333333333 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 = -1.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 0.25 + -1x + x2 = -1.083333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -1.083333333 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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