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Simplifying 20v2 + -27vr + 9r2 = 0 Reorder the terms: -27rv + 9r2 + 20v2 = 0 Solving -27rv + 9r2 + 20v2 = 0 Solving for variable 'r'. Factor a trinomial. (3r + -5v)(3r + -4v) = 0Subproblem 1
Set the factor '(3r + -5v)' equal to zero and attempt to solve: Simplifying 3r + -5v = 0 Solving 3r + -5v = 0 Move all terms containing r to the left, all other terms to the right. Add '5v' to each side of the equation. 3r + -5v + 5v = 0 + 5v Combine like terms: -5v + 5v = 0 3r + 0 = 0 + 5v 3r = 0 + 5v Remove the zero: 3r = 5v Divide each side by '3'. r = 1.666666667v Simplifying r = 1.666666667vSubproblem 2
Set the factor '(3r + -4v)' equal to zero and attempt to solve: Simplifying 3r + -4v = 0 Solving 3r + -4v = 0 Move all terms containing r to the left, all other terms to the right. Add '4v' to each side of the equation. 3r + -4v + 4v = 0 + 4v Combine like terms: -4v + 4v = 0 3r + 0 = 0 + 4v 3r = 0 + 4v Remove the zero: 3r = 4v Divide each side by '3'. r = 1.333333333v Simplifying r = 1.333333333vSolution
r = {1.666666667v, 1.333333333v}
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