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Simplifying 20r2 + -20rs + -15s2 = 0 Reorder the terms: -20rs + 20r2 + -15s2 = 0 Solving -20rs + 20r2 + -15s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4rs + 4r2 + -3s2) = 0 Factor a trinomial. 5((2r + -3s)(2r + s)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2r + -3s)' equal to zero and attempt to solve: Simplifying 2r + -3s = 0 Solving 2r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. 2r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 2r + 0 = 0 + 3s 2r = 0 + 3s Remove the zero: 2r = 3s Divide each side by '2'. r = 1.5s Simplifying r = 1.5sSubproblem 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 = {1.5s, -0.5s}
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