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Simplifying -3k2 + 2k + -17 = -4k2 + 7 Reorder the terms: -17 + 2k + -3k2 = -4k2 + 7 Reorder the terms: -17 + 2k + -3k2 = 7 + -4k2 Solving -17 + 2k + -3k2 = 7 + -4k2 Solving for variable 'k'. Reorder the terms: -17 + -7 + 2k + -3k2 + 4k2 = 7 + -4k2 + -7 + 4k2 Combine like terms: -17 + -7 = -24 -24 + 2k + -3k2 + 4k2 = 7 + -4k2 + -7 + 4k2 Combine like terms: -3k2 + 4k2 = 1k2 -24 + 2k + 1k2 = 7 + -4k2 + -7 + 4k2 Reorder the terms: -24 + 2k + 1k2 = 7 + -7 + -4k2 + 4k2 Combine like terms: 7 + -7 = 0 -24 + 2k + 1k2 = 0 + -4k2 + 4k2 -24 + 2k + 1k2 = -4k2 + 4k2 Combine like terms: -4k2 + 4k2 = 0 -24 + 2k + 1k2 = 0 Factor a trinomial. (-6 + -1k)(4 + -1k) = 0Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve: Simplifying -6 + -1k = 0 Solving -6 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1k = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1k = 0 + 6 -1k = 0 + 6 Combine like terms: 0 + 6 = 6 -1k = 6 Divide each side by '-1'. k = -6 Simplifying k = -6Subproblem 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 = {-6, 4}
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