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Simplifying 0 = 12a3 + -6a2 + 18a Reorder the terms: 0 = 18a + -6a2 + 12a3 Solving 0 = 18a + -6a2 + 12a3 Solving for variable 'a'. Remove the zero: -18a + 6a2 + -12a3 = 18a + -6a2 + 12a3 + -18a + 6a2 + -12a3 Reorder the terms: -18a + 6a2 + -12a3 = 18a + -18a + -6a2 + 6a2 + 12a3 + -12a3 Combine like terms: 18a + -18a = 0 -18a + 6a2 + -12a3 = 0 + -6a2 + 6a2 + 12a3 + -12a3 -18a + 6a2 + -12a3 = -6a2 + 6a2 + 12a3 + -12a3 Combine like terms: -6a2 + 6a2 = 0 -18a + 6a2 + -12a3 = 0 + 12a3 + -12a3 -18a + 6a2 + -12a3 = 12a3 + -12a3 Combine like terms: 12a3 + -12a3 = 0 -18a + 6a2 + -12a3 = 0 Factor out the Greatest Common Factor (GCF), '6a'. 6a(-3 + a + -2a2) = 0 Ignore the factor 6.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 '(-3 + a + -2a2)' equal to zero and attempt to solve: Simplifying -3 + a + -2a2 = 0 Solving -3 + a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -0.5a + a2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.5a + -1.5 + a2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.5a + a2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.5a + a2 = 0 + -1.5 -0.5a + a2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.5a + a2 = -1.5 The a term is a. 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. -0.5a + 0.25 + a2 = -1.5 + 0.25 Reorder the terms: 0.25 + -0.5a + a2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + -0.5a + a2 = -1.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -1.25 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.Solution
a = {0}
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