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Simplifying 4k2 + 5k + 4 = -3k Reorder the terms: 4 + 5k + 4k2 = -3k Solving 4 + 5k + 4k2 = -3k Solving for variable 'k'. Reorder the terms: 4 + 5k + 3k + 4k2 = -3k + 3k Combine like terms: 5k + 3k = 8k 4 + 8k + 4k2 = -3k + 3k Combine like terms: -3k + 3k = 0 4 + 8k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 2k + k2) = 0 Factor a trinomial. 4((1 + k)(1 + k)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Solution
k = {-1, -1}
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