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Simplifying v2 + 8vf + 15f2 = 0 Reorder the terms: 8fv + 15f2 + v2 = 0 Solving 8fv + 15f2 + v2 = 0 Solving for variable 'f'. Factor a trinomial. (5f + v)(3f + v) = 0Subproblem 1
Set the factor '(5f + v)' equal to zero and attempt to solve: Simplifying 5f + v = 0 Solving 5f + v = 0 Move all terms containing f to the left, all other terms to the right. Add '-1v' to each side of the equation. 5f + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 5f + 0 = 0 + -1v 5f = 0 + -1v Remove the zero: 5f = -1v Divide each side by '5'. f = -0.2v Simplifying f = -0.2vSubproblem 2
Set the factor '(3f + v)' equal to zero and attempt to solve: Simplifying 3f + v = 0 Solving 3f + v = 0 Move all terms containing f to the left, all other terms to the right. Add '-1v' to each side of the equation. 3f + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 3f + 0 = 0 + -1v 3f = 0 + -1v Remove the zero: 3f = -1v Divide each side by '3'. f = -0.3333333333v Simplifying f = -0.3333333333vSolution
f = {-0.2v, -0.3333333333v}
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