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Simplifying (n + -8)(n + -8) = 169 Reorder the terms: (-8 + n)(n + -8) = 169 Reorder the terms: (-8 + n)(-8 + n) = 169 Multiply (-8 + n) * (-8 + n) (-8(-8 + n) + n(-8 + n)) = 169 ((-8 * -8 + n * -8) + n(-8 + n)) = 169 ((64 + -8n) + n(-8 + n)) = 169 (64 + -8n + (-8 * n + n * n)) = 169 (64 + -8n + (-8n + n2)) = 169 Combine like terms: -8n + -8n = -16n (64 + -16n + n2) = 169 Solving 64 + -16n + n2 = 169 Solving for variable 'n'. Reorder the terms: 64 + -169 + -16n + n2 = 169 + -169 Combine like terms: 64 + -169 = -105 -105 + -16n + n2 = 169 + -169 Combine like terms: 169 + -169 = 0 -105 + -16n + n2 = 0 Factor a trinomial. (-5 + -1n)(21 + -1n) = 0Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve: Simplifying -5 + -1n = 0 Solving -5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n = 0 + 5 -1n = 0 + 5 Combine like terms: 0 + 5 = 5 -1n = 5 Divide each side by '-1'. n = -5 Simplifying n = -5Subproblem 2
Set the factor '(21 + -1n)' equal to zero and attempt to solve: Simplifying 21 + -1n = 0 Solving 21 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1n = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1n = 0 + -21 -1n = 0 + -21 Combine like terms: 0 + -21 = -21 -1n = -21 Divide each side by '-1'. n = 21 Simplifying n = 21Solution
n = {-5, 21}
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