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Simplifying 3a2 + -1af + -4f2 = 0 Reorder the terms: -1af + 3a2 + -4f2 = 0 Solving -1af + 3a2 + -4f2 = 0 Solving for variable 'a'. Factor a trinomial. (3a + -4f)(a + f) = 0Subproblem 1
Set the factor '(3a + -4f)' equal to zero and attempt to solve: Simplifying 3a + -4f = 0 Solving 3a + -4f = 0 Move all terms containing a to the left, all other terms to the right. Add '4f' to each side of the equation. 3a + -4f + 4f = 0 + 4f Combine like terms: -4f + 4f = 0 3a + 0 = 0 + 4f 3a = 0 + 4f Remove the zero: 3a = 4f Divide each side by '3'. a = 1.333333333f Simplifying a = 1.333333333fSubproblem 2
Set the factor '(a + f)' equal to zero and attempt to solve: Simplifying a + f = 0 Solving a + f = 0 Move all terms containing a to the left, all other terms to the right. Add '-1f' to each side of the equation. a + f + -1f = 0 + -1f Combine like terms: f + -1f = 0 a + 0 = 0 + -1f a = 0 + -1f Remove the zero: a = -1f Simplifying a = -1fSolution
a = {1.333333333f, -1f}
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