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Simplifying -12a7 + 9a6 + -3a5 = 0 Reorder the terms: -3a5 + 9a6 + -12a7 = 0 Solving -3a5 + 9a6 + -12a7 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a5'. 3a5(-1 + 3a + -4a2) = 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 + -4a2)' equal to zero and attempt to solve: Simplifying -1 + 3a + -4a2 = 0 Solving -1 + 3a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.25 + -0.75a + a2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.75a + -0.25 + a2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.75a + a2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.75a + a2 = 0 + -0.25 -0.75a + a2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.75a + a2 = -0.25 The a term is -0.75a. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75a + 0.140625 + a2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + -0.75a + a2 = -0.109375 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = -0.109375 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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