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Simplifying 81r2 + -180rt + 100t2 = 0 Reorder the terms: -180rt + 81r2 + 100t2 = 0 Solving -180rt + 81r2 + 100t2 = 0 Solving for variable 'r'. Factor a trinomial. (9r + -10t)(9r + -10t) = 0Subproblem 1
Set the factor '(9r + -10t)' equal to zero and attempt to solve: Simplifying 9r + -10t = 0 Solving 9r + -10t = 0 Move all terms containing r to the left, all other terms to the right. Add '10t' to each side of the equation. 9r + -10t + 10t = 0 + 10t Combine like terms: -10t + 10t = 0 9r + 0 = 0 + 10t 9r = 0 + 10t Remove the zero: 9r = 10t Divide each side by '9'. r = 1.111111111t Simplifying r = 1.111111111tSubproblem 2
Set the factor '(9r + -10t)' equal to zero and attempt to solve: Simplifying 9r + -10t = 0 Solving 9r + -10t = 0 Move all terms containing r to the left, all other terms to the right. Add '10t' to each side of the equation. 9r + -10t + 10t = 0 + 10t Combine like terms: -10t + 10t = 0 9r + 0 = 0 + 10t 9r = 0 + 10t Remove the zero: 9r = 10t Divide each side by '9'. r = 1.111111111t Simplifying r = 1.111111111tSolution
r = {1.111111111t, 1.111111111t}
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