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Simplifying 2a9 + -32a = 0 Reorder the terms: -32a + 2a9 = 0 Solving -32a + 2a9 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-16 + a8) = 0 Factor a difference between two squares. 2a((4 + a4)(-4 + a4)) = 0 Factor a difference between two squares. 2a((4 + a4)((2 + a2)(-2 + a2))) = 0 Ignore the factor 2.Subproblem 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 '(4 + a4)' equal to zero and attempt to solve: Simplifying 4 + a4 = 0 Solving 4 + a4 = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a4 = 0 + -4 a4 = 0 + -4 Combine like terms: 0 + -4 = -4 a4 = -4 Simplifying a4 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + a2)' equal to zero and attempt to solve: Simplifying 2 + a2 = 0 Solving 2 + a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a2 = 0 + -2 a2 = 0 + -2 Combine like terms: 0 + -2 = -2 a2 = -2 Simplifying a2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(-2 + a2)' equal to zero and attempt to solve: Simplifying -2 + a2 = 0 Solving -2 + a2 = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + a2 = 0 + 2 a2 = 0 + 2 Combine like terms: 0 + 2 = 2 a2 = 2 Simplifying a2 = 2 Take the square root of each side: a = {-1.414213562, 1.414213562}Solution
a = {0, -1.414213562, 1.414213562}
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