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Simplifying -10r2 + 25rs + 8rs + -20s2 = 0 Reorder the terms: 25rs + 8rs + -10r2 + -20s2 = 0 Combine like terms: 25rs + 8rs = 33rs 33rs + -10r2 + -20s2 = 0 Solving 33rs + -10r2 + -20s2 = 0 Solving for variable 'r'. Factor a trinomial. (-5r + 4s)(2r + -5s) = 0Subproblem 1
Set the factor '(-5r + 4s)' equal to zero and attempt to solve: Simplifying -5r + 4s = 0 Solving -5r + 4s = 0 Move all terms containing r to the left, all other terms to the right. Add '-4s' to each side of the equation. -5r + 4s + -4s = 0 + -4s Combine like terms: 4s + -4s = 0 -5r + 0 = 0 + -4s -5r = 0 + -4s Remove the zero: -5r = -4s Divide each side by '-5'. r = 0.8s Simplifying r = 0.8sSubproblem 2
Set the factor '(2r + -5s)' equal to zero and attempt to solve: Simplifying 2r + -5s = 0 Solving 2r + -5s = 0 Move all terms containing r to the left, all other terms to the right. Add '5s' to each side of the equation. 2r + -5s + 5s = 0 + 5s Combine like terms: -5s + 5s = 0 2r + 0 = 0 + 5s 2r = 0 + 5s Remove the zero: 2r = 5s Divide each side by '2'. r = 2.5s Simplifying r = 2.5sSolution
r = {0.8s, 2.5s}
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