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Simplifying 20r2 + -12rs + 25rs + -15s2 = 0 Reorder the terms: -12rs + 25rs + 20r2 + -15s2 = 0 Combine like terms: -12rs + 25rs = 13rs 13rs + 20r2 + -15s2 = 0 Solving 13rs + 20r2 + -15s2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + -3s)(4r + 5s) = 0Subproblem 1
Set the factor '(5r + -3s)' equal to zero and attempt to solve: Simplifying 5r + -3s = 0 Solving 5r + -3s = 0 Move all terms containing r to the left, all other terms to the right. Add '3s' to each side of the equation. 5r + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 5r + 0 = 0 + 3s 5r = 0 + 3s Remove the zero: 5r = 3s Divide each side by '5'. r = 0.6s Simplifying r = 0.6sSubproblem 2
Set the factor '(4r + 5s)' equal to zero and attempt to solve: Simplifying 4r + 5s = 0 Solving 4r + 5s = 0 Move all terms containing r to the left, all other terms to the right. Add '-5s' to each side of the equation. 4r + 5s + -5s = 0 + -5s Combine like terms: 5s + -5s = 0 4r + 0 = 0 + -5s 4r = 0 + -5s Remove the zero: 4r = -5s Divide each side by '4'. r = -1.25s Simplifying r = -1.25sSolution
r = {0.6s, -1.25s}
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