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Simplifying 3k4 + 10k2 + -25 = 0 Reorder the terms: -25 + 10k2 + 3k4 = 0 Solving -25 + 10k2 + 3k4 = 0 Solving for variable 'k'. Factor a trinomial. (-5 + -1k2)(5 + -3k2) = 0Subproblem 1
Set the factor '(-5 + -1k2)' equal to zero and attempt to solve: Simplifying -5 + -1k2 = 0 Solving -5 + -1k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1k2 = 0 + 5 -1k2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1k2 = 5 Divide each side by '-1'. k2 = -5 Simplifying k2 = -5 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 '(5 + -3k2)' equal to zero and attempt to solve: Simplifying 5 + -3k2 = 0 Solving 5 + -3k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k2 = 0 + -5 -3k2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3k2 = -5 Divide each side by '-3'. k2 = 1.666666667 Simplifying k2 = 1.666666667 Take the square root of each side: k = {-1.290994449, 1.290994449}Solution
k = {-1.290994449, 1.290994449}
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