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Simplifying 5k4 + 8k3 + -4k2 = 0 Reorder the terms: -4k2 + 8k3 + 5k4 = 0 Solving -4k2 + 8k3 + 5k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k2'. k2(-4 + 8k + 5k2) = 0 Factor a trinomial. k2((-2 + -1k)(2 + -5k)) = 0Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve: Simplifying k2 = 0 Solving k2 = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k2 = 0 Take the square root of each side: k = {0}Subproblem 2
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 3
Set the factor '(2 + -5k)' equal to zero and attempt to solve: Simplifying 2 + -5k = 0 Solving 2 + -5k = 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 + -5k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5k = 0 + -2 -5k = 0 + -2 Combine like terms: 0 + -2 = -2 -5k = -2 Divide each side by '-5'. k = 0.4 Simplifying k = 0.4Solution
k = {0, -2, 0.4}
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