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Simplifying (3x3 + 2x2 + -5x) + (-8x3 + 3x) = 0 Reorder the terms: (-5x + 2x2 + 3x3) + (-8x3 + 3x) = 0 Remove parenthesis around (-5x + 2x2 + 3x3) -5x + 2x2 + 3x3 + (-8x3 + 3x) = 0 Reorder the terms: -5x + 2x2 + 3x3 + (3x + -8x3) = 0 Remove parenthesis around (3x + -8x3) -5x + 2x2 + 3x3 + 3x + -8x3 = 0 Reorder the terms: -5x + 3x + 2x2 + 3x3 + -8x3 = 0 Combine like terms: -5x + 3x = -2x -2x + 2x2 + 3x3 + -8x3 = 0 Combine like terms: 3x3 + -8x3 = -5x3 -2x + 2x2 + -5x3 = 0 Solving -2x + 2x2 + -5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 2x + -5x2) = 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 '(-2 + 2x + -5x2)' equal to zero and attempt to solve: Simplifying -2 + 2x + -5x2 = 0 Solving -2 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.4 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.4x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.4x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.4x + x2 = 0 + -0.4 -0.4x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.4x + x2 = -0.4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.4 + 0.04 Combine like terms: -0.4 + 0.04 = -0.36 0.04 + -0.4x + x2 = -0.36 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = -0.36 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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