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Simplifying 25r2 + 40rf + 16f2 = 0 Reorder the terms: 40fr + 16f2 + 25r2 = 0 Solving 40fr + 16f2 + 25r2 = 0 Solving for variable 'f'. Factor a trinomial. (4f + 5r)(4f + 5r) = 0Subproblem 1
Set the factor '(4f + 5r)' equal to zero and attempt to solve: Simplifying 4f + 5r = 0 Solving 4f + 5r = 0 Move all terms containing f to the left, all other terms to the right. Add '-5r' to each side of the equation. 4f + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 4f + 0 = 0 + -5r 4f = 0 + -5r Remove the zero: 4f = -5r Divide each side by '4'. f = -1.25r Simplifying f = -1.25rSubproblem 2
Set the factor '(4f + 5r)' equal to zero and attempt to solve: Simplifying 4f + 5r = 0 Solving 4f + 5r = 0 Move all terms containing f to the left, all other terms to the right. Add '-5r' to each side of the equation. 4f + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 4f + 0 = 0 + -5r 4f = 0 + -5r Remove the zero: 4f = -5r Divide each side by '4'. f = -1.25r Simplifying f = -1.25rSolution
f = {-1.25r, -1.25r}
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