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Simplifying 8r2 + -10rs + -3s2 = 0 Reorder the terms: -10rs + 8r2 + -3s2 = 0 Solving -10rs + 8r2 + -3s2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + -3s)(4r + s) = 0Subproblem 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 '(4r + s)' equal to zero and attempt to solve: Simplifying 4r + s = 0 Solving 4r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 4r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 4r + 0 = 0 + -1s 4r = 0 + -1s Remove the zero: 4r = -1s Divide each side by '4'. r = -0.25s Simplifying r = -0.25sSolution
r = {1.5s, -0.25s}
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