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Simplifying r2 + 3rf + -28f2 = 0 Reorder the terms: 3fr + -28f2 + r2 = 0 Solving 3fr + -28f2 + r2 = 0 Solving for variable 'f'. Factor a trinomial. (-7f + -1r)(4f + -1r) = 0Subproblem 1
Set the factor '(-7f + -1r)' equal to zero and attempt to solve: Simplifying -7f + -1r = 0 Solving -7f + -1r = 0 Move all terms containing f to the left, all other terms to the right. Add 'r' to each side of the equation. -7f + -1r + r = 0 + r Combine like terms: -1r + r = 0 -7f + 0 = 0 + r -7f = 0 + r Remove the zero: -7f = r Divide each side by '-7'. f = -0.1428571429r Simplifying f = -0.1428571429rSubproblem 2
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 = 0.25rSolution
f = {-0.1428571429r, 0.25r}
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