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Simplifying s2 + -3sf + -40f2 = 0 Reorder the terms: -3fs + -40f2 + s2 = 0 Solving -3fs + -40f2 + s2 = 0 Solving for variable 'f'. Factor a trinomial. (-5f + -1s)(8f + -1s) = 0Subproblem 1
Set the factor '(-5f + -1s)' equal to zero and attempt to solve: Simplifying -5f + -1s = 0 Solving -5f + -1s = 0 Move all terms containing f to the left, all other terms to the right. Add 's' to each side of the equation. -5f + -1s + s = 0 + s Combine like terms: -1s + s = 0 -5f + 0 = 0 + s -5f = 0 + s Remove the zero: -5f = s Divide each side by '-5'. f = -0.2s Simplifying f = -0.2sSubproblem 2
Set the factor '(8f + -1s)' equal to zero and attempt to solve: Simplifying 8f + -1s = 0 Solving 8f + -1s = 0 Move all terms containing f to the left, all other terms to the right. Add 's' to each side of the equation. 8f + -1s + s = 0 + s Combine like terms: -1s + s = 0 8f + 0 = 0 + s 8f = 0 + s Remove the zero: 8f = s Divide each side by '8'. f = 0.125s Simplifying f = 0.125sSolution
f = {-0.2s, 0.125s}
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