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Simplifying 0 = k2 + 4k + 4 Reorder the terms: 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 out the Greatest Common Factor (GCF), '-1'. -1(4 + 4k + k2) = 0 Factor a trinomial. -1((2 + k)(2 + k)) = 0 Ignore the factor -1.Subproblem 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 + 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 = {-2, -2}
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