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Simplifying 16x3 + -6x2 + 4x = 0 Reorder the terms: 4x + -6x2 + 16x3 = 0 Solving 4x + -6x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(2 + -3x + 8x2) = 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 '(2 + -3x + 8x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + 8x2 = 0 Solving 2 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -0.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.375x + x2 = 0 + -0.25 -0.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.375x + x2 = -0.25 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = -0.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = -0.25 + 0.03515625 Combine like terms: -0.25 + 0.03515625 = -0.21484375 0.03515625 + -0.375x + x2 = -0.21484375 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = -0.21484375 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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