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Simplifying k4 + -8k2 + 15 = 0 Reorder the terms: 15 + -8k2 + k4 = 0 Solving 15 + -8k2 + k4 = 0 Solving for variable 'k'. Factor a trinomial. (3 + -1k2)(5 + -1k2) = 0Subproblem 1
Set the factor '(3 + -1k2)' equal to zero and attempt to solve: Simplifying 3 + -1k2 = 0 Solving 3 + -1k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k2 = 0 + -3 -1k2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1k2 = -3 Divide each side by '-1'. k2 = 3 Simplifying k2 = 3 Take the square root of each side: k = {-1.732050808, 1.732050808}Subproblem 2
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 Take the square root of each side: k = {-2.236067978, 2.236067978}Solution
k = {-1.732050808, 1.732050808, -2.236067978, 2.236067978}
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