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Simplifying (16x3 + -1x2 + 3x) + (-12x3 + 3x2 + 2x) = 0 Reorder the terms: (3x + -1x2 + 16x3) + (-12x3 + 3x2 + 2x) = 0 Remove parenthesis around (3x + -1x2 + 16x3) 3x + -1x2 + 16x3 + (-12x3 + 3x2 + 2x) = 0 Reorder the terms: 3x + -1x2 + 16x3 + (2x + 3x2 + -12x3) = 0 Remove parenthesis around (2x + 3x2 + -12x3) 3x + -1x2 + 16x3 + 2x + 3x2 + -12x3 = 0 Reorder the terms: 3x + 2x + -1x2 + 3x2 + 16x3 + -12x3 = 0 Combine like terms: 3x + 2x = 5x 5x + -1x2 + 3x2 + 16x3 + -12x3 = 0 Combine like terms: -1x2 + 3x2 = 2x2 5x + 2x2 + 16x3 + -12x3 = 0 Combine like terms: 16x3 + -12x3 = 4x3 5x + 2x2 + 4x3 = 0 Solving 5x + 2x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 2x + 4x2) = 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 '(5 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 4x2 = 0 Solving 5 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.5x + x2 = 0 + -1.25 0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.5x + x2 = -1.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + 0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -1.1875 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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