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Simplifying (3a2 + -5a + -9) + (6a2 + 2a + 12) = 0 Reorder the terms: (-9 + -5a + 3a2) + (6a2 + 2a + 12) = 0 Remove parenthesis around (-9 + -5a + 3a2) -9 + -5a + 3a2 + (6a2 + 2a + 12) = 0 Reorder the terms: -9 + -5a + 3a2 + (12 + 2a + 6a2) = 0 Remove parenthesis around (12 + 2a + 6a2) -9 + -5a + 3a2 + 12 + 2a + 6a2 = 0 Reorder the terms: -9 + 12 + -5a + 2a + 3a2 + 6a2 = 0 Combine like terms: -9 + 12 = 3 3 + -5a + 2a + 3a2 + 6a2 = 0 Combine like terms: -5a + 2a = -3a 3 + -3a + 3a2 + 6a2 = 0 Combine like terms: 3a2 + 6a2 = 9a2 3 + -3a + 9a2 = 0 Solving 3 + -3a + 9a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -1a + 3a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1a + 3a2)' equal to zero and attempt to solve: Simplifying 1 + -1a + 3a2 = 0 Solving 1 + -1a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -0.3333333333a + a2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.3333333333a + -0.3333333333 + a2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.3333333333a + a2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.3333333333a + a2 = 0 + -0.3333333333 -0.3333333333a + a2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.3333333333a + a2 = -0.3333333333 The a term is -0.3333333333a. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333a + 0.02777777779 + a2 = -0.3333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333a + a2 = -0.3333333333 + 0.02777777779 Combine like terms: -0.3333333333 + 0.02777777779 = -0.30555555551 0.02777777779 + -0.3333333333a + a2 = -0.30555555551 Factor a perfect square on the left side: (a + -0.1666666667)(a + -0.1666666667) = -0.30555555551 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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