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Simplifying r2 + -2rf + -24f2 = 0 Reorder the terms: -2fr + -24f2 + r2 = 0 Solving -2fr + -24f2 + r2 = 0 Solving for variable 'f'. Factor a trinomial. (-4f + -1r)(6f + -1r) = 0Subproblem 1
Set the factor '(-4f + -1r)' equal to zero and attempt to solve: Simplifying -4f + -1r = 0 Solving -4f + -1r = 0 Move all terms containing f to the left, all other terms to the right. Add 'r' to each side of the equation. -4f + -1r + r = 0 + r Combine like terms: -1r + r = 0 -4f + 0 = 0 + r -4f = 0 + r Remove the zero: -4f = r Divide each side by '-4'. f = -0.25r Simplifying f = -0.25rSubproblem 2
Set the factor '(6f + -1r)' equal to zero and attempt to solve: Simplifying 6f + -1r = 0 Solving 6f + -1r = 0 Move all terms containing f to the left, all other terms to the right. Add 'r' to each side of the equation. 6f + -1r + r = 0 + r Combine like terms: -1r + r = 0 6f + 0 = 0 + r 6f = 0 + r Remove the zero: 6f = r Divide each side by '6'. f = 0.1666666667r Simplifying f = 0.1666666667rSolution
f = {-0.25r, 0.1666666667r}
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