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Simplifying 2f(a) = 5a2 + 4a Multiply f * a 2af = 5a2 + 4a Reorder the terms: 2af = 4a + 5a2 Solving 2af = 4a + 5a2 Solving for variable 'a'. Reorder the terms: -4a + 2af + -5a2 = 4a + 5a2 + -4a + -5a2 Reorder the terms: -4a + 2af + -5a2 = 4a + -4a + 5a2 + -5a2 Combine like terms: 4a + -4a = 0 -4a + 2af + -5a2 = 0 + 5a2 + -5a2 -4a + 2af + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 -4a + 2af + -5a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-4 + 2f + -5a) = 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 '(-4 + 2f + -5a)' equal to zero and attempt to solve: Simplifying -4 + 2f + -5a = 0 Reorder the terms: -4 + -5a + 2f = 0 Solving -4 + -5a + 2f = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -5a + 4 + 2f = 0 + 4 Reorder the terms: -4 + 4 + -5a + 2f = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5a + 2f = 0 + 4 -5a + 2f = 0 + 4 Combine like terms: 0 + 4 = 4 -5a + 2f = 4 Add '-2f' to each side of the equation. -5a + 2f + -2f = 4 + -2f Combine like terms: 2f + -2f = 0 -5a + 0 = 4 + -2f -5a = 4 + -2f Divide each side by '-5'. a = -0.8 + 0.4f Simplifying a = -0.8 + 0.4fSolution
a = {0, -0.8 + 0.4f}
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