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Simplifying 64x3 + -16x2 + 12x = 0 Reorder the terms: 12x + -16x2 + 64x3 = 0 Solving 12x + -16x2 + 64x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + -4x + 16x2) = 0 Ignore the factor 4.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 '(3 + -4x + 16x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 16x2 = 0 Solving 3 + -4x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -0.25x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -0.25x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -0.25x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -0.25x + x2 = 0 + -0.1875 -0.25x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -0.25x + x2 = -0.1875 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -0.1875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -0.1875 + 0.015625 Combine like terms: -0.1875 + 0.015625 = -0.171875 0.015625 + -0.25x + x2 = -0.171875 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = -0.171875 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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