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Simplifying k4 + -7k2 + 10 = 0 Reorder the terms: 10 + -7k2 + k4 = 0 Solving 10 + -7k2 + k4 = 0 Solving for variable 'k'. Factor a trinomial. (2 + -1k2)(5 + -1k2) = 0Subproblem 1
Set the factor '(2 + -1k2)' equal to zero and attempt to solve: Simplifying 2 + -1k2 = 0 Solving 2 + -1k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k2 = 0 + -2 -1k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1k2 = -2 Divide each side by '-1'. k2 = 2 Simplifying k2 = 2 Take the square root of each side: k = {-1.414213562, 1.414213562}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 = {-1.414213562, 1.414213562, -2.236067978, 2.236067978}
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