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Simplifying 3k4 + k2 + -4 = 0 Reorder the terms: -4 + k2 + 3k4 = 0 Solving -4 + k2 + 3k4 = 0 Solving for variable 'k'. Factor a trinomial. (-4 + -3k2)(1 + -1k2) = 0 Factor a difference between two squares. (-4 + -3k2)((1 + k)(1 + -1k)) = 0Subproblem 1
Set the factor '(-4 + -3k2)' equal to zero and attempt to solve: Simplifying -4 + -3k2 = 0 Solving -4 + -3k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3k2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3k2 = 0 + 4 -3k2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3k2 = 4 Divide each side by '-3'. k2 = -1.333333333 Simplifying k2 = -1.333333333 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 '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Subproblem 3
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Solution
k = {-1, 1}
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