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Simplifying 12r2 + -16s2 + -26rs = 0 Reorder the terms: -26rs + 12r2 + -16s2 = 0 Solving -26rs + 12r2 + -16s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13rs + 6r2 + -8s2) = 0 Factor a trinomial. 2((3r + -8s)(2r + s)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3r + -8s)' equal to zero and attempt to solve: Simplifying 3r + -8s = 0 Solving 3r + -8s = 0 Move all terms containing r to the left, all other terms to the right. Add '8s' to each side of the equation. 3r + -8s + 8s = 0 + 8s Combine like terms: -8s + 8s = 0 3r + 0 = 0 + 8s 3r = 0 + 8s Remove the zero: 3r = 8s Divide each side by '3'. r = 2.666666667s Simplifying r = 2.666666667sSubproblem 2
Set the factor '(2r + s)' equal to zero and attempt to solve: Simplifying 2r + s = 0 Solving 2r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 2r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 2r + 0 = 0 + -1s 2r = 0 + -1s Remove the zero: 2r = -1s Divide each side by '2'. r = -0.5s Simplifying r = -0.5sSolution
r = {2.666666667s, -0.5s}
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