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Simplifying 18a2 + 24ap + 8p2 = 0 Reorder the terms: 24ap + 18a2 + 8p2 = 0 Solving 24ap + 18a2 + 8p2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(12ap + 9a2 + 4p2) = 0 Factor a trinomial. 2((3a + 2p)(3a + 2p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3a + 2p)' equal to zero and attempt to solve: Simplifying 3a + 2p = 0 Solving 3a + 2p = 0 Move all terms containing a to the left, all other terms to the right. Add '-2p' to each side of the equation. 3a + 2p + -2p = 0 + -2p Combine like terms: 2p + -2p = 0 3a + 0 = 0 + -2p 3a = 0 + -2p Remove the zero: 3a = -2p Divide each side by '3'. a = -0.6666666667p Simplifying a = -0.6666666667pSubproblem 2
Set the factor '(3a + 2p)' equal to zero and attempt to solve: Simplifying 3a + 2p = 0 Solving 3a + 2p = 0 Move all terms containing a to the left, all other terms to the right. Add '-2p' to each side of the equation. 3a + 2p + -2p = 0 + -2p Combine like terms: 2p + -2p = 0 3a + 0 = 0 + -2p 3a = 0 + -2p Remove the zero: 3a = -2p Divide each side by '3'. a = -0.6666666667p Simplifying a = -0.6666666667pSolution
a = {-0.6666666667p, -0.6666666667p}
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