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Simplifying a3 = 81a Solving a3 = 81a Solving for variable 'a'. Reorder the terms: -81a + a3 = 81a + -81a Combine like terms: 81a + -81a = 0 -81a + a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-81 + a2) = 0 Factor a difference between two squares. a((9 + a)(-9 + a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve: Simplifying 9 + a = 0 Solving 9 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + a = 0 + -9 a = 0 + -9 Combine like terms: 0 + -9 = -9 a = -9 Simplifying a = -9Subproblem 3
Set the factor '(-9 + a)' equal to zero and attempt to solve: Simplifying -9 + a = 0 Solving -9 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + a = 0 + 9 a = 0 + 9 Combine like terms: 0 + 9 = 9 a = 9 Simplifying a = 9Solution
a = {0, -9, 9}
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