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Simplifying 4k2 = 48k + -128 Reorder the terms: 4k2 = -128 + 48k Solving 4k2 = -128 + 48k Solving for variable 'k'. Reorder the terms: 128 + -48k + 4k2 = -128 + 48k + 128 + -48k Reorder the terms: 128 + -48k + 4k2 = -128 + 128 + 48k + -48k Combine like terms: -128 + 128 = 0 128 + -48k + 4k2 = 0 + 48k + -48k 128 + -48k + 4k2 = 48k + -48k Combine like terms: 48k + -48k = 0 128 + -48k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(32 + -12k + k2) = 0 Factor a trinomial. 4((4 + -1k)(8 + -1k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4Subproblem 2
Set the factor '(8 + -1k)' equal to zero and attempt to solve: Simplifying 8 + -1k = 0 Solving 8 + -1k = 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 + -1k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1k = 0 + -8 -1k = 0 + -8 Combine like terms: 0 + -8 = -8 -1k = -8 Divide each side by '-1'. k = 8 Simplifying k = 8Solution
k = {4, 8}
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