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Simplifying 3a3 + 18a2 + 36a = 0 Reorder the terms: 36a + 18a2 + 3a3 = 0 Solving 36a + 18a2 + 3a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(12 + 6a + a2) = 0 Ignore the factor 3.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 '(12 + 6a + a2)' equal to zero and attempt to solve: Simplifying 12 + 6a + a2 = 0 Solving 12 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 6a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + 6a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6a + a2 = 0 + -12 6a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 6a + a2 = -12 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = -12 + 9 Reorder the terms: 9 + 6a + a2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + 6a + a2 = -3 Factor a perfect square on the left side: (a + 3)(a + 3) = -3 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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