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Simplifying 3ab + 6a2b + 9b = 0 Solving 3ab + 6a2b + 9b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(a + 2a2 + 3) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b = 0 + -1b Remove the zero: 0 = -1b Simplifying 0 = -1b 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 '(a + 2a2 + 3)' equal to zero and attempt to solve: Simplifying a + 2a2 + 3 = 0 Reorder the terms: 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. The solution to this equation could not be determined.
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