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Simplifying 10r2s2 + 9rst + 2t2 = 0 Reorder the terms: 9rst + 10r2s2 + 2t2 = 0 Solving 9rst + 10r2s2 + 2t2 = 0 Solving for variable 'r'. Factor a trinomial. (5rs + 2t)(2rs + t) = 0Subproblem 1
Set the factor '(5rs + 2t)' equal to zero and attempt to solve: Simplifying 5rs + 2t = 0 Solving 5rs + 2t = 0 Move all terms containing r to the left, all other terms to the right. Add '-2t' to each side of the equation. 5rs + 2t + -2t = 0 + -2t Combine like terms: 2t + -2t = 0 5rs + 0 = 0 + -2t 5rs = 0 + -2t Remove the zero: 5rs = -2t Divide each side by '5s'. r = -0.4s-1t Simplifying r = -0.4s-1tSubproblem 2
Set the factor '(2rs + t)' equal to zero and attempt to solve: Simplifying 2rs + t = 0 Solving 2rs + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-1t' to each side of the equation. 2rs + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 2rs + 0 = 0 + -1t 2rs = 0 + -1t Remove the zero: 2rs = -1t Divide each side by '2s'. r = -0.5s-1t Simplifying r = -0.5s-1tSolution
r = {-0.4s-1t, -0.5s-1t}
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