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Simplifying 3k4 + 10k3 + -48k2 = 0 Reorder the terms: -48k2 + 10k3 + 3k4 = 0 Solving -48k2 + 10k3 + 3k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k2'. k2(-48 + 10k + 3k2) = 0 Factor a trinomial. k2((-6 + -1k)(8 + -3k)) = 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 '(-6 + -1k)' equal to zero and attempt to solve: Simplifying -6 + -1k = 0 Solving -6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1k = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1k = 0 + 6 -1k = 0 + 6 Combine like terms: 0 + 6 = 6 -1k = 6 Divide each side by '-1'. k = -6 Simplifying k = -6Subproblem 3
Set the factor '(8 + -3k)' equal to zero and attempt to solve: Simplifying 8 + -3k = 0 Solving 8 + -3k = 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 + -3k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3k = 0 + -8 -3k = 0 + -8 Combine like terms: 0 + -8 = -8 -3k = -8 Divide each side by '-3'. k = 2.666666667 Simplifying k = 2.666666667Solution
k = {0, -6, 2.666666667}
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