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Simplifying -9a7 + 9a6 + -3a5 = 0 Reorder the terms: -3a5 + 9a6 + -9a7 = 0 Solving -3a5 + 9a6 + -9a7 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a5'. 3a5(-1 + 3a + -3a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a5' equal to zero and attempt to solve: Simplifying a5 = 0 Solving a5 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a5 = 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 + 3a + -3a2)' equal to zero and attempt to solve: Simplifying -1 + 3a + -3a2 = 0 Solving -1 + 3a + -3a2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -1a + a2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -1a + -0.3333333333 + a2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -1a + a2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -1a + a2 = 0 + -0.3333333333 -1a + a2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -1a + a2 = -0.3333333333 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 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + -1a + a2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + -1a + a2 = -0.0833333333 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = -0.0833333333 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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