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Simplifying (k + 7)(k + 7) = 289 Reorder the terms: (7 + k)(k + 7) = 289 Reorder the terms: (7 + k)(7 + k) = 289 Multiply (7 + k) * (7 + k) (7(7 + k) + k(7 + k)) = 289 ((7 * 7 + k * 7) + k(7 + k)) = 289 ((49 + 7k) + k(7 + k)) = 289 (49 + 7k + (7 * k + k * k)) = 289 (49 + 7k + (7k + k2)) = 289 Combine like terms: 7k + 7k = 14k (49 + 14k + k2) = 289 Solving 49 + 14k + k2 = 289 Solving for variable 'k'. Reorder the terms: 49 + -289 + 14k + k2 = 289 + -289 Combine like terms: 49 + -289 = -240 -240 + 14k + k2 = 289 + -289 Combine like terms: 289 + -289 = 0 -240 + 14k + k2 = 0 Factor a trinomial. (-24 + -1k)(10 + -1k) = 0Subproblem 1
Set the factor '(-24 + -1k)' equal to zero and attempt to solve: Simplifying -24 + -1k = 0 Solving -24 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1k = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1k = 0 + 24 -1k = 0 + 24 Combine like terms: 0 + 24 = 24 -1k = 24 Divide each side by '-1'. k = -24 Simplifying k = -24Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve: Simplifying 10 + -1k = 0 Solving 10 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1k = 0 + -10 -1k = 0 + -10 Combine like terms: 0 + -10 = -10 -1k = -10 Divide each side by '-1'. k = 10 Simplifying k = 10Solution
k = {-24, 10}
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