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Simplifying k2 + 5k + -7 = 3 + 8k Reorder the terms: -7 + 5k + k2 = 3 + 8k Solving -7 + 5k + k2 = 3 + 8k Solving for variable 'k'. Reorder the terms: -7 + -3 + 5k + -8k + k2 = 3 + 8k + -3 + -8k Combine like terms: -7 + -3 = -10 -10 + 5k + -8k + k2 = 3 + 8k + -3 + -8k Combine like terms: 5k + -8k = -3k -10 + -3k + k2 = 3 + 8k + -3 + -8k Reorder the terms: -10 + -3k + k2 = 3 + -3 + 8k + -8k Combine like terms: 3 + -3 = 0 -10 + -3k + k2 = 0 + 8k + -8k -10 + -3k + k2 = 8k + -8k Combine like terms: 8k + -8k = 0 -10 + -3k + k2 = 0 Factor a trinomial. (-2 + -1k)(5 + -1k) = 0Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5Solution
k = {-2, 5}
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