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Simplifying 36a3 + -24a4 + 60a5 = 0 Solving 36a3 + -24a4 + 60a5 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '12a3'. 12a3(3 + -2a + 5a2) = 0 Ignore the factor 12.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 + -2a + 5a2)' equal to zero and attempt to solve: Simplifying 3 + -2a + 5a2 = 0 Solving 3 + -2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -0.4a + a2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -0.4a + -0.6 + a2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -0.4a + a2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -0.4a + a2 = 0 + -0.6 -0.4a + a2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -0.4a + a2 = -0.6 The a term is -0.4a. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4a + 0.04 + a2 = -0.6 + 0.04 Reorder the terms: 0.04 + -0.4a + a2 = -0.6 + 0.04 Combine like terms: -0.6 + 0.04 = -0.56 0.04 + -0.4a + a2 = -0.56 Factor a perfect square on the left side: (a + -0.2)(a + -0.2) = -0.56 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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