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Simplifying (5a + -3f)(5a + 2f) = 0 Multiply (5a + -3f) * (5a + 2f) (5a * (5a + 2f) + -3f * (5a + 2f)) = 0 ((5a * 5a + 2f * 5a) + -3f * (5a + 2f)) = 0 Reorder the terms: ((10af + 25a2) + -3f * (5a + 2f)) = 0 ((10af + 25a2) + -3f * (5a + 2f)) = 0 (10af + 25a2 + (5a * -3f + 2f * -3f)) = 0 (10af + 25a2 + (-15af + -6f2)) = 0 Reorder the terms: (10af + -15af + 25a2 + -6f2) = 0 Combine like terms: 10af + -15af = -5af (-5af + 25a2 + -6f2) = 0 Solving -5af + 25a2 + -6f2 = 0 Solving for variable 'a'. Factor a trinomial. (5a + -3f)(5a + 2f) = 0Subproblem 1
Set the factor '(5a + -3f)' equal to zero and attempt to solve: Simplifying 5a + -3f = 0 Solving 5a + -3f = 0 Move all terms containing a to the left, all other terms to the right. Add '3f' to each side of the equation. 5a + -3f + 3f = 0 + 3f Combine like terms: -3f + 3f = 0 5a + 0 = 0 + 3f 5a = 0 + 3f Remove the zero: 5a = 3f Divide each side by '5'. a = 0.6f Simplifying a = 0.6fSubproblem 2
Set the factor '(5a + 2f)' equal to zero and attempt to solve: Simplifying 5a + 2f = 0 Solving 5a + 2f = 0 Move all terms containing a to the left, all other terms to the right. Add '-2f' to each side of the equation. 5a + 2f + -2f = 0 + -2f Combine like terms: 2f + -2f = 0 5a + 0 = 0 + -2f 5a = 0 + -2f Remove the zero: 5a = -2f Divide each side by '5'. a = -0.4f Simplifying a = -0.4fSolution
a = {0.6f, -0.4f}
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