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Simplifying r4 + -81 = 0 Reorder the terms: -81 + r4 = 0 Solving -81 + r4 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + r4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + r4 = 0 + 81 r4 = 0 + 81 Combine like terms: 0 + 81 = 81 r4 = 81 Simplifying r4 = 81 Reorder the terms: -81 + r4 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + r4 = 0 Factor a difference between two squares. (9 + r2)(-9 + r2) = 0 Factor a difference between two squares. (9 + r2)((3 + r)(-3 + r)) = 0Subproblem 1
Set the factor '(9 + r2)' equal to zero and attempt to solve: Simplifying 9 + r2 = 0 Solving 9 + r2 = 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 + r2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + r2 = 0 + -9 r2 = 0 + -9 Combine like terms: 0 + -9 = -9 r2 = -9 Simplifying r2 = -9 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 '(3 + r)' equal to zero and attempt to solve: Simplifying 3 + r = 0 Solving 3 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r = 0 + -3 r = 0 + -3 Combine like terms: 0 + -3 = -3 r = -3 Simplifying r = -3Subproblem 3
Set the factor '(-3 + r)' equal to zero and attempt to solve: Simplifying -3 + r = 0 Solving -3 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + r = 0 + 3 r = 0 + 3 Combine like terms: 0 + 3 = 3 r = 3 Simplifying r = 3Solution
r = {-3, 3}
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