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Simplifying 4a3 + -16a2 + 32a = 0 Reorder the terms: 32a + -16a2 + 4a3 = 0 Solving 32a + -16a2 + 4a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(8 + -4a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(8 + -4a + a2)' equal to zero and attempt to solve: Simplifying 8 + -4a + a2 = 0 Solving 8 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -4a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -4a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -4a + a2 = 0 + -8 -4a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -4a + a2 = -8 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = -8 + 4 Reorder the terms: 4 + -4a + a2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + -4a + a2 = -4 Factor a perfect square on the left side: (a + -2)(a + -2) = -4 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
a = {0}
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