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Simplifying w2 + -2wf + -63f2 = 0 Reorder the terms: -2fw + -63f2 + w2 = 0 Solving -2fw + -63f2 + w2 = 0 Solving for variable 'f'. Factor a trinomial. (-7f + -1w)(9f + -1w) = 0Subproblem 1
Set the factor '(-7f + -1w)' equal to zero and attempt to solve: Simplifying -7f + -1w = 0 Solving -7f + -1w = 0 Move all terms containing f to the left, all other terms to the right. Add 'w' to each side of the equation. -7f + -1w + w = 0 + w Combine like terms: -1w + w = 0 -7f + 0 = 0 + w -7f = 0 + w Remove the zero: -7f = w Divide each side by '-7'. f = -0.1428571429w Simplifying f = -0.1428571429wSubproblem 2
Set the factor '(9f + -1w)' equal to zero and attempt to solve: Simplifying 9f + -1w = 0 Solving 9f + -1w = 0 Move all terms containing f to the left, all other terms to the right. Add 'w' to each side of the equation. 9f + -1w + w = 0 + w Combine like terms: -1w + w = 0 9f + 0 = 0 + w 9f = 0 + w Remove the zero: 9f = w Divide each side by '9'. f = 0.1111111111w Simplifying f = 0.1111111111wSolution
f = {-0.1428571429w, 0.1111111111w}
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