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Simplifying 25r2 + 90rt + 81t2 = 0 Reorder the terms: 90rt + 25r2 + 81t2 = 0 Solving 90rt + 25r2 + 81t2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + 9t)(5r + 9t) = 0Subproblem 1
Set the factor '(5r + 9t)' equal to zero and attempt to solve: Simplifying 5r + 9t = 0 Solving 5r + 9t = 0 Move all terms containing r to the left, all other terms to the right. Add '-9t' to each side of the equation. 5r + 9t + -9t = 0 + -9t Combine like terms: 9t + -9t = 0 5r + 0 = 0 + -9t 5r = 0 + -9t Remove the zero: 5r = -9t Divide each side by '5'. r = -1.8t Simplifying r = -1.8tSubproblem 2
Set the factor '(5r + 9t)' equal to zero and attempt to solve: Simplifying 5r + 9t = 0 Solving 5r + 9t = 0 Move all terms containing r to the left, all other terms to the right. Add '-9t' to each side of the equation. 5r + 9t + -9t = 0 + -9t Combine like terms: 9t + -9t = 0 5r + 0 = 0 + -9t 5r = 0 + -9t Remove the zero: 5r = -9t Divide each side by '5'. r = -1.8t Simplifying r = -1.8tSolution
r = {-1.8t, -1.8t}
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