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Simplifying a3 + -1(2a3 + -1(4a + -5a3)) = 0 a3 + -1(2a3 + (4a * -1 + -5a3 * -1)) = 0 a3 + -1(2a3 + (-4a + 5a3)) = 0 Reorder the terms: a3 + -1(-4a + 2a3 + 5a3) = 0 Combine like terms: 2a3 + 5a3 = 7a3 a3 + -1(-4a + 7a3) = 0 a3 + (-4a * -1 + 7a3 * -1) = 0 a3 + (4a + -7a3) = 0 Reorder the terms: 4a + a3 + -7a3 = 0 Combine like terms: a3 + -7a3 = -6a3 4a + -6a3 = 0 Solving 4a + -6a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(2 + -3a2) = 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 '(2 + -3a2)' equal to zero and attempt to solve: Simplifying 2 + -3a2 = 0 Solving 2 + -3a2 = 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 + -3a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a2 = 0 + -2 -3a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3a2 = -2 Divide each side by '-3'. a2 = 0.6666666667 Simplifying a2 = 0.6666666667 Take the square root of each side: a = {-0.816496581, 0.816496581}Solution
a = {0, -0.816496581, 0.816496581}
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