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Simplifying 75a2 + 90ag + 27g2 = 0 Reorder the terms: 90ag + 75a2 + 27g2 = 0 Solving 90ag + 75a2 + 27g2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(30ag + 25a2 + 9g2) = 0 Factor a trinomial. 3((5a + 3g)(5a + 3g)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5a + 3g)' equal to zero and attempt to solve: Simplifying 5a + 3g = 0 Solving 5a + 3g = 0 Move all terms containing a to the left, all other terms to the right. Add '-3g' to each side of the equation. 5a + 3g + -3g = 0 + -3g Combine like terms: 3g + -3g = 0 5a + 0 = 0 + -3g 5a = 0 + -3g Remove the zero: 5a = -3g Divide each side by '5'. a = -0.6g Simplifying a = -0.6gSubproblem 2
Set the factor '(5a + 3g)' equal to zero and attempt to solve: Simplifying 5a + 3g = 0 Solving 5a + 3g = 0 Move all terms containing a to the left, all other terms to the right. Add '-3g' to each side of the equation. 5a + 3g + -3g = 0 + -3g Combine like terms: 3g + -3g = 0 5a + 0 = 0 + -3g 5a = 0 + -3g Remove the zero: 5a = -3g Divide each side by '5'. a = -0.6g Simplifying a = -0.6gSolution
a = {-0.6g, -0.6g}
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