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Simplifying -2k2 + 19 = 8k + -3k2 + 3 Reorder the terms: 19 + -2k2 = 8k + -3k2 + 3 Reorder the terms: 19 + -2k2 = 3 + 8k + -3k2 Solving 19 + -2k2 = 3 + 8k + -3k2 Solving for variable 'k'. Reorder the terms: 19 + -3 + -8k + -2k2 + 3k2 = 3 + 8k + -3k2 + -3 + -8k + 3k2 Combine like terms: 19 + -3 = 16 16 + -8k + -2k2 + 3k2 = 3 + 8k + -3k2 + -3 + -8k + 3k2 Combine like terms: -2k2 + 3k2 = 1k2 16 + -8k + 1k2 = 3 + 8k + -3k2 + -3 + -8k + 3k2 Reorder the terms: 16 + -8k + 1k2 = 3 + -3 + 8k + -8k + -3k2 + 3k2 Combine like terms: 3 + -3 = 0 16 + -8k + 1k2 = 0 + 8k + -8k + -3k2 + 3k2 16 + -8k + 1k2 = 8k + -8k + -3k2 + 3k2 Combine like terms: 8k + -8k = 0 16 + -8k + 1k2 = 0 + -3k2 + 3k2 16 + -8k + 1k2 = -3k2 + 3k2 Combine like terms: -3k2 + 3k2 = 0 16 + -8k + 1k2 = 0 Factor a trinomial. (4 + -1k)(4 + -1k) = 0Subproblem 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 '(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 = 4Solution
k = {4, 4}
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