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Simplifying 8r2 + 20rs + 10rs + 25s2 = 0 Reorder the terms: 20rs + 10rs + 8r2 + 25s2 = 0 Combine like terms: 20rs + 10rs = 30rs 30rs + 8r2 + 25s2 = 0 Solving 30rs + 8r2 + 25s2 = 0 Solving for variable 'r'. Factor a trinomial. (4r + 5s)(2r + 5s) = 0Subproblem 1
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 = -1.25sSubproblem 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 = {-1.25s, -2.5s}
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