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Simplifying 4k2 + 8k + 4 + -8k2 + 28 = 0 Reorder the terms: 4 + 28 + 8k + 4k2 + -8k2 = 0 Combine like terms: 4 + 28 = 32 32 + 8k + 4k2 + -8k2 = 0 Combine like terms: 4k2 + -8k2 = -4k2 32 + 8k + -4k2 = 0 Solving 32 + 8k + -4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 2k + -1k2) = 0 Factor a trinomial. 4((4 + -1k)(2 + k)) = 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 '(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 = -2Solution
k = {4, -2}
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