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Simplifying 5w2 + -1wf + -6f2 = 0 Reorder the terms: -1fw + -6f2 + 5w2 = 0 Solving -1fw + -6f2 + 5w2 = 0 Solving for variable 'f'. Factor a trinomial. (-1f + -1w)(6f + -5w) = 0Subproblem 1
Set the factor '(-1f + -1w)' equal to zero and attempt to solve: Simplifying -1f + -1w = 0 Solving -1f + -1w = 0 Move all terms containing f to the left, all other terms to the right. Add 'w' to each side of the equation. -1f + -1w + w = 0 + w Combine like terms: -1w + w = 0 -1f + 0 = 0 + w -1f = 0 + w Remove the zero: -1f = w Divide each side by '-1'. f = -1w Simplifying f = -1wSubproblem 2
Set the factor '(6f + -5w)' equal to zero and attempt to solve: Simplifying 6f + -5w = 0 Solving 6f + -5w = 0 Move all terms containing f to the left, all other terms to the right. Add '5w' to each side of the equation. 6f + -5w + 5w = 0 + 5w Combine like terms: -5w + 5w = 0 6f + 0 = 0 + 5w 6f = 0 + 5w Remove the zero: 6f = 5w Divide each side by '6'. f = 0.8333333333w Simplifying f = 0.8333333333wSolution
f = {-1w, 0.8333333333w}
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