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Simplifying 5k4 + 22k2 + -48 = 0 Reorder the terms: -48 + 22k2 + 5k4 = 0 Solving -48 + 22k2 + 5k4 = 0 Solving for variable 'k'. Factor a trinomial. (-6 + -1k2)(8 + -5k2) = 0Subproblem 1
Set the factor '(-6 + -1k2)' equal to zero and attempt to solve: Simplifying -6 + -1k2 = 0 Solving -6 + -1k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1k2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1k2 = 0 + 6 -1k2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1k2 = 6 Divide each side by '-1'. k2 = -6 Simplifying k2 = -6 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 '(8 + -5k2)' equal to zero and attempt to solve: Simplifying 8 + -5k2 = 0 Solving 8 + -5k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k2 = 0 + -8 -5k2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5k2 = -8 Divide each side by '-5'. k2 = 1.6 Simplifying k2 = 1.6 Take the square root of each side: k = {-1.264911064, 1.264911064}Solution
k = {-1.264911064, 1.264911064}
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