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Simplifying 4r2 + 9rt + 5t2 = 0 Reorder the terms: 9rt + 4r2 + 5t2 = 0 Solving 9rt + 4r2 + 5t2 = 0 Solving for variable 'r'. Factor a trinomial. (r + t)(4r + 5t) = 0Subproblem 1
Set the factor '(r + t)' equal to zero and attempt to solve: Simplifying r + t = 0 Solving r + t = 0 Move all terms containing r to the left, all other terms to the right. Add '-1t' to each side of the equation. r + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 r + 0 = 0 + -1t r = 0 + -1t Remove the zero: r = -1t Simplifying r = -1tSubproblem 2
Set the factor '(4r + 5t)' equal to zero and attempt to solve: Simplifying 4r + 5t = 0 Solving 4r + 5t = 0 Move all terms containing r to the left, all other terms to the right. Add '-5t' to each side of the equation. 4r + 5t + -5t = 0 + -5t Combine like terms: 5t + -5t = 0 4r + 0 = 0 + -5t 4r = 0 + -5t Remove the zero: 4r = -5t Divide each side by '4'. r = -1.25t Simplifying r = -1.25tSolution
r = {-1t, -1.25t}
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