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Simplifying w2 + -2wf + -24f2 = 0 Reorder the terms: -2fw + -24f2 + w2 = 0 Solving -2fw + -24f2 + w2 = 0 Solving for variable 'f'. Factor a trinomial. (-4f + -1w)(6f + -1w) = 0Subproblem 1
Set the factor '(-4f + -1w)' equal to zero and attempt to solve: Simplifying -4f + -1w = 0 Solving -4f + -1w = 0 Move all terms containing f to the left, all other terms to the right. Add 'w' to each side of the equation. -4f + -1w + w = 0 + w Combine like terms: -1w + w = 0 -4f + 0 = 0 + w -4f = 0 + w Remove the zero: -4f = w Divide each side by '-4'. f = -0.25w Simplifying f = -0.25wSubproblem 2
Set the factor '(6f + -1w)' equal to zero and attempt to solve: Simplifying 6f + -1w = 0 Solving 6f + -1w = 0 Move all terms containing f to the left, all other terms to the right. Add 'w' to each side of the equation. 6f + -1w + w = 0 + w Combine like terms: -1w + w = 0 6f + 0 = 0 + w 6f = 0 + w Remove the zero: 6f = w Divide each side by '6'. f = 0.1666666667w Simplifying f = 0.1666666667wSolution
f = {-0.25w, 0.1666666667w}
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