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Simplifying -6a5 + 6a4 + -3a3 = 0 Reorder the terms: -3a3 + 6a4 + -6a5 = 0 Solving -3a3 + 6a4 + -6a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a3'. 3a3(-1 + 2a + -2a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve: Simplifying a3 = 0 Solving a3 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + 2a + -2a2)' equal to zero and attempt to solve: Simplifying -1 + 2a + -2a2 = 0 Solving -1 + 2a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -1a + a2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1a + -0.5 + a2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1a + a2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1a + a2 = 0 + -0.5 -1a + a2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1a + a2 = -0.5 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1a + a2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1a + a2 = -0.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = -0.25 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. The solution to this equation could not be determined.
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