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Simplifying (k + -3)(k + -1) = 24 Reorder the terms: (-3 + k)(k + -1) = 24 Reorder the terms: (-3 + k)(-1 + k) = 24 Multiply (-3 + k) * (-1 + k) (-3(-1 + k) + k(-1 + k)) = 24 ((-1 * -3 + k * -3) + k(-1 + k)) = 24 ((3 + -3k) + k(-1 + k)) = 24 (3 + -3k + (-1 * k + k * k)) = 24 (3 + -3k + (-1k + k2)) = 24 Combine like terms: -3k + -1k = -4k (3 + -4k + k2) = 24 Solving 3 + -4k + k2 = 24 Solving for variable 'k'. Reorder the terms: 3 + -24 + -4k + k2 = 24 + -24 Combine like terms: 3 + -24 = -21 -21 + -4k + k2 = 24 + -24 Combine like terms: 24 + -24 = 0 -21 + -4k + k2 = 0 Factor a trinomial. (-3 + -1k)(7 + -1k) = 0Subproblem 1
Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7Solution
k = {-3, 7}
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