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Simplifying 6k4 + -1k2 + -1 = 0 Reorder the terms: -1 + -1k2 + 6k4 = 0 Solving -1 + -1k2 + 6k4 = 0 Solving for variable 'k'. Factor a trinomial. (-1 + -3k2)(1 + -2k2) = 0Subproblem 1
Set the factor '(-1 + -3k2)' equal to zero and attempt to solve: Simplifying -1 + -3k2 = 0 Solving -1 + -3k2 = 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 + -3k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3k2 = 0 + 1 -3k2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3k2 = 1 Divide each side by '-3'. k2 = -0.3333333333 Simplifying k2 = -0.3333333333 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 + -2k2)' equal to zero and attempt to solve: Simplifying 1 + -2k2 = 0 Solving 1 + -2k2 = 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 + -2k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2k2 = 0 + -1 -2k2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2k2 = -1 Divide each side by '-2'. k2 = 0.5 Simplifying k2 = 0.5 Take the square root of each side: k = {-0.707106781, 0.707106781}Solution
k = {-0.707106781, 0.707106781}
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