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Simplifying 50r2 + 40rf + 8f2 = 0 Reorder the terms: 40fr + 8f2 + 50r2 = 0 Solving 40fr + 8f2 + 50r2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2'. 2(20fr + 4f2 + 25r2) = 0 Factor a trinomial. 2((2f + 5r)(2f + 5r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2f + 5r)' equal to zero and attempt to solve: Simplifying 2f + 5r = 0 Solving 2f + 5r = 0 Move all terms containing f to the left, all other terms to the right. Add '-5r' to each side of the equation. 2f + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 2f + 0 = 0 + -5r 2f = 0 + -5r Remove the zero: 2f = -5r Divide each side by '2'. f = -2.5r Simplifying f = -2.5rSubproblem 2
Set the factor '(2f + 5r)' equal to zero and attempt to solve: Simplifying 2f + 5r = 0 Solving 2f + 5r = 0 Move all terms containing f to the left, all other terms to the right. Add '-5r' to each side of the equation. 2f + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 2f + 0 = 0 + -5r 2f = 0 + -5r Remove the zero: 2f = -5r Divide each side by '2'. f = -2.5r Simplifying f = -2.5rSolution
f = {-2.5r, -2.5r}
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