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Simplifying (2k + 8)(2k + 8) = 0 Reorder the terms: (8 + 2k)(2k + 8) = 0 Reorder the terms: (8 + 2k)(8 + 2k) = 0 Multiply (8 + 2k) * (8 + 2k) (8(8 + 2k) + 2k * (8 + 2k)) = 0 ((8 * 8 + 2k * 8) + 2k * (8 + 2k)) = 0 ((64 + 16k) + 2k * (8 + 2k)) = 0 (64 + 16k + (8 * 2k + 2k * 2k)) = 0 (64 + 16k + (16k + 4k2)) = 0 Combine like terms: 16k + 16k = 32k (64 + 32k + 4k2) = 0 Solving 64 + 32k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + 8k + k2) = 0 Factor a trinomial. 4((4 + k)(4 + k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + k)' equal to zero and attempt to solve: Simplifying 4 + k = 0 Solving 4 + k = 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 + k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + k = 0 + -4 k = 0 + -4 Combine like terms: 0 + -4 = -4 k = -4 Simplifying k = -4Subproblem 2
Set the factor '(4 + k)' equal to zero and attempt to solve: Simplifying 4 + k = 0 Solving 4 + k = 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 + k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + k = 0 + -4 k = 0 + -4 Combine like terms: 0 + -4 = -4 k = -4 Simplifying k = -4Solution
k = {-4, -4}
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