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Simplifying 9t2 + 24tr + 16r2 = 0 Reorder the terms: 24rt + 16r2 + 9t2 = 0 Solving 24rt + 16r2 + 9t2 = 0 Solving for variable 'r'. Factor a trinomial. (4r + 3t)(4r + 3t) = 0Subproblem 1
Set the factor '(4r + 3t)' equal to zero and attempt to solve: Simplifying 4r + 3t = 0 Solving 4r + 3t = 0 Move all terms containing r to the left, all other terms to the right. Add '-3t' to each side of the equation. 4r + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 4r + 0 = 0 + -3t 4r = 0 + -3t Remove the zero: 4r = -3t Divide each side by '4'. r = -0.75t Simplifying r = -0.75tSubproblem 2
Set the factor '(4r + 3t)' equal to zero and attempt to solve: Simplifying 4r + 3t = 0 Solving 4r + 3t = 0 Move all terms containing r to the left, all other terms to the right. Add '-3t' to each side of the equation. 4r + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 4r + 0 = 0 + -3t 4r = 0 + -3t Remove the zero: 4r = -3t Divide each side by '4'. r = -0.75t Simplifying r = -0.75tSolution
r = {-0.75t, -0.75t}
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