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Simplifying 0 = 4 + -4k + k2 Solving 0 = 4 + -4k + k2 Solving for variable 'k'. Combine like terms: 0 + -4 = -4 -4 + 4k + -1k2 = 4 + -4k + k2 + -4 + 4k + -1k2 Reorder the terms: -4 + 4k + -1k2 = 4 + -4 + -4k + 4k + k2 + -1k2 Combine like terms: 4 + -4 = 0 -4 + 4k + -1k2 = 0 + -4k + 4k + k2 + -1k2 -4 + 4k + -1k2 = -4k + 4k + k2 + -1k2 Combine like terms: -4k + 4k = 0 -4 + 4k + -1k2 = 0 + k2 + -1k2 -4 + 4k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -4 + 4k + -1k2 = 0 Factor a trinomial. (-2 + k)(2 + -1k) = 0Subproblem 1
Set the factor '(-2 + k)' equal to zero and attempt to solve: Simplifying -2 + k = 0 Solving -2 + k = 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 + k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + k = 0 + 2 k = 0 + 2 Combine like terms: 0 + 2 = 2 k = 2 Simplifying k = 2Subproblem 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 = 2Solution
k = {2, 2}
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