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Simplifying 14r2 + -31rt + 15t2 = 0 Reorder the terms: -31rt + 14r2 + 15t2 = 0 Solving -31rt + 14r2 + 15t2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + -3t)(7r + -5t) = 0Subproblem 1
Set the factor '(2r + -3t)' equal to zero and attempt to solve: Simplifying 2r + -3t = 0 Solving 2r + -3t = 0 Move all terms containing r to the left, all other terms to the right. Add '3t' to each side of the equation. 2r + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 2r + 0 = 0 + 3t 2r = 0 + 3t Remove the zero: 2r = 3t Divide each side by '2'. r = 1.5t Simplifying r = 1.5tSubproblem 2
Set the factor '(7r + -5t)' equal to zero and attempt to solve: Simplifying 7r + -5t = 0 Solving 7r + -5t = 0 Move all terms containing r to the left, all other terms to the right. Add '5t' to each side of the equation. 7r + -5t + 5t = 0 + 5t Combine like terms: -5t + 5t = 0 7r + 0 = 0 + 5t 7r = 0 + 5t Remove the zero: 7r = 5t Divide each side by '7'. r = 0.7142857143t Simplifying r = 0.7142857143tSolution
r = {1.5t, 0.7142857143t}
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