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Simplifying 45r2 + -120rs + 80s2 = 0 Reorder the terms: -120rs + 45r2 + 80s2 = 0 Solving -120rs + 45r2 + 80s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(-24rs + 9r2 + 16s2) = 0 Factor a trinomial. 5((3r + -4s)(3r + -4s)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3r + -4s)' equal to zero and attempt to solve: Simplifying 3r + -4s = 0 Solving 3r + -4s = 0 Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 3r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 3r + 0 = 0 + 4s 3r = 0 + 4s Remove the zero: 3r = 4s Divide each side by '3'. r = 1.333333333s Simplifying r = 1.333333333sSubproblem 2
Set the factor '(3r + -4s)' equal to zero and attempt to solve: Simplifying 3r + -4s = 0 Solving 3r + -4s = 0 Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 3r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 3r + 0 = 0 + 4s 3r = 0 + 4s Remove the zero: 3r = 4s Divide each side by '3'. r = 1.333333333s Simplifying r = 1.333333333sSolution
r = {1.333333333s, 1.333333333s}
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