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Simplifying 8k2 + -80k4 = -192 Solving 8k2 + -80k4 = -192 Solving for variable 'k'. Reorder the terms: 192 + 8k2 + -80k4 = -192 + 192 Combine like terms: -192 + 192 = 0 192 + 8k2 + -80k4 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(24 + k2 + -10k4) = 0 Factor a trinomial. 8((8 + -5k2)(3 + 2k2)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(8 + -5k2)' equal to zero and attempt to solve: Simplifying 8 + -5k2 = 0 Solving 8 + -5k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k2 = 0 + -8 -5k2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5k2 = -8 Divide each side by '-5'. k2 = 1.6 Simplifying k2 = 1.6 Take the square root of each side: k = {-1.264911064, 1.264911064}Subproblem 2
Set the factor '(3 + 2k2)' equal to zero and attempt to solve: Simplifying 3 + 2k2 = 0 Solving 3 + 2k2 = 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 + 2k2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2k2 = 0 + -3 2k2 = 0 + -3 Combine like terms: 0 + -3 = -3 2k2 = -3 Divide each side by '2'. k2 = -1.5 Simplifying k2 = -1.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {-1.264911064, 1.264911064}
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