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Simplifying g(a) = 5a2 + -8a Multiply g * a ag = 5a2 + -8a Reorder the terms: ag = -8a + 5a2 Solving ag = -8a + 5a2 Solving for variable 'a'. Reorder the terms: 8a + ag + -5a2 = -8a + 5a2 + 8a + -5a2 Reorder the terms: 8a + ag + -5a2 = -8a + 8a + 5a2 + -5a2 Combine like terms: -8a + 8a = 0 8a + ag + -5a2 = 0 + 5a2 + -5a2 8a + ag + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 8a + ag + -5a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(8 + g + -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 '(8 + g + -5a)' equal to zero and attempt to solve: Simplifying 8 + g + -5a = 0 Reorder the terms: 8 + -5a + g = 0 Solving 8 + -5a + g = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -5a + -8 + g = 0 + -8 Reorder the terms: 8 + -8 + -5a + g = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5a + g = 0 + -8 -5a + g = 0 + -8 Combine like terms: 0 + -8 = -8 -5a + g = -8 Add '-1g' to each side of the equation. -5a + g + -1g = -8 + -1g Combine like terms: g + -1g = 0 -5a + 0 = -8 + -1g -5a = -8 + -1g Divide each side by '-5'. a = 1.6 + 0.2g Simplifying a = 1.6 + 0.2gSolution
a = {0, 1.6 + 0.2g}
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