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Simplifying (6k2 + -1)(6k2 + -1) = 0 Reorder the terms: (-1 + 6k2)(6k2 + -1) = 0 Reorder the terms: (-1 + 6k2)(-1 + 6k2) = 0 Multiply (-1 + 6k2) * (-1 + 6k2) (-1(-1 + 6k2) + 6k2 * (-1 + 6k2)) = 0 ((-1 * -1 + 6k2 * -1) + 6k2 * (-1 + 6k2)) = 0 ((1 + -6k2) + 6k2 * (-1 + 6k2)) = 0 (1 + -6k2 + (-1 * 6k2 + 6k2 * 6k2)) = 0 (1 + -6k2 + (-6k2 + 36k4)) = 0 Combine like terms: -6k2 + -6k2 = -12k2 (1 + -12k2 + 36k4) = 0 Solving 1 + -12k2 + 36k4 = 0 Solving for variable 'k'. Factor a trinomial. (1 + -6k2)(1 + -6k2) = 0Subproblem 1
Set the factor '(1 + -6k2)' equal to zero and attempt to solve: Simplifying 1 + -6k2 = 0 Solving 1 + -6k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6k2 = 0 + -1 -6k2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6k2 = -1 Divide each side by '-6'. k2 = 0.1666666667 Simplifying k2 = 0.1666666667 Take the square root of each side: k = {-0.408248291, 0.408248291}Subproblem 2
Set the factor '(1 + -6k2)' equal to zero and attempt to solve: Simplifying 1 + -6k2 = 0 Solving 1 + -6k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6k2 = 0 + -1 -6k2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6k2 = -1 Divide each side by '-6'. k2 = 0.1666666667 Simplifying k2 = 0.1666666667 Take the square root of each side: k = {-0.408248291, 0.408248291}Solution
k = {-0.408248291, 0.408248291, -0.408248291, 0.408248291}
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