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Simplifying k4 + -81 = 0 Reorder the terms: -81 + k4 = 0 Solving -81 + k4 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + k4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + k4 = 0 + 81 k4 = 0 + 81 Combine like terms: 0 + 81 = 81 k4 = 81 Simplifying k4 = 81 Reorder the terms: -81 + k4 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + k4 = 0 Factor a difference between two squares. (9 + k2)(-9 + k2) = 0 Factor a difference between two squares. (9 + k2)((3 + k)(-3 + k)) = 0Subproblem 1
Set the factor '(9 + k2)' equal to zero and attempt to solve: Simplifying 9 + k2 = 0 Solving 9 + k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + k2 = 0 + -9 k2 = 0 + -9 Combine like terms: 0 + -9 = -9 k2 = -9 Simplifying k2 = -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 + k)' equal to zero and attempt to solve: Simplifying 3 + k = 0 Solving 3 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k = 0 + -3 k = 0 + -3 Combine like terms: 0 + -3 = -3 k = -3 Simplifying k = -3Subproblem 3
Set the factor '(-3 + k)' equal to zero and attempt to solve: Simplifying -3 + k = 0 Solving -3 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + k = 0 + 3 k = 0 + 3 Combine like terms: 0 + 3 = 3 k = 3 Simplifying k = 3Solution
k = {-3, 3}
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