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Simplifying 9a5 + -12a4 + 9a3 = 0 Reorder the terms: 9a3 + -12a4 + 9a5 = 0 Solving 9a3 + -12a4 + 9a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a3'. 3a3(3 + -4a + 3a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve: Simplifying a3 = 0 Solving a3 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3 = 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 '(3 + -4a + 3a2)' equal to zero and attempt to solve: Simplifying 3 + -4a + 3a2 = 0 Solving 3 + -4a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -1.333333333a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.333333333a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -1.333333333a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.333333333a + a2 = 0 + -1 -1.333333333a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.333333333a + a2 = -1 The a term is -1.333333333a. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333a + 0.4444444442 + a2 = -1 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333a + a2 = -1 + 0.4444444442 Combine like terms: -1 + 0.4444444442 = -0.5555555558 0.4444444442 + -1.333333333a + a2 = -0.5555555558 Factor a perfect square on the left side: (a + -0.6666666665)(a + -0.6666666665) = -0.5555555558 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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