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Simplifying k2 = 32 + -4k Solving k2 = 32 + -4k Solving for variable 'k'. Reorder the terms: -32 + 4k + k2 = 32 + -4k + -32 + 4k Reorder the terms: -32 + 4k + k2 = 32 + -32 + -4k + 4k Combine like terms: 32 + -32 = 0 -32 + 4k + k2 = 0 + -4k + 4k -32 + 4k + k2 = -4k + 4k Combine like terms: -4k + 4k = 0 -32 + 4k + k2 = 0 Factor a trinomial. (-8 + -1k)(4 + -1k) = 0Subproblem 1
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 = -8Subproblem 2
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 = 4Solution
k = {-8, 4}
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