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Simplifying 14r3t2 + 38r2t2 + -72rt2 = 0 Reorder the terms: -72rt2 + 38r2t2 + 14r3t2 = 0 Solving -72rt2 + 38r2t2 + 14r3t2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2rt2'. 2rt2(-36 + 19r + 7r2) = 0 Factor a trinomial. 2rt2((-4 + -1r)(9 + -7r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'rt2' equal to zero and attempt to solve: Simplifying rt2 = 0 Solving rt2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying rt2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 3
Set the factor '(9 + -7r)' equal to zero and attempt to solve: Simplifying 9 + -7r = 0 Solving 9 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7r = 0 + -9 -7r = 0 + -9 Combine like terms: 0 + -9 = -9 -7r = -9 Divide each side by '-7'. r = 1.285714286 Simplifying r = 1.285714286Solution
r = {-4, 1.285714286}
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