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Simplifying k4 + -7k2 + -144 = 0 Reorder the terms: -144 + -7k2 + k4 = 0 Solving -144 + -7k2 + k4 = 0 Solving for variable 'k'. Factor a trinomial. (-9 + -1k2)(16 + -1k2) = 0 Factor a difference between two squares. (-9 + -1k2)((4 + k)(4 + -1k)) = 0Subproblem 1
Set the factor '(-9 + -1k2)' equal to zero and attempt to solve: Simplifying -9 + -1k2 = 0 Solving -9 + -1k2 = 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 + -1k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1k2 = 0 + 9 -1k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1k2 = 9 Divide each side by '-1'. 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 '(4 + k)' equal to zero and attempt to solve: Simplifying 4 + k = 0 Solving 4 + k = 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 + k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + k = 0 + -4 k = 0 + -4 Combine like terms: 0 + -4 = -4 k = -4 Simplifying k = -4Subproblem 3
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 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 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Solution
k = {-4, 4}
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