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Simplifying n2 + -16n + 24 = 9 Reorder the terms: 24 + -16n + n2 = 9 Solving 24 + -16n + n2 = 9 Solving for variable 'n'. Reorder the terms: 24 + -9 + -16n + n2 = 9 + -9 Combine like terms: 24 + -9 = 15 15 + -16n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 15 + -16n + n2 = 0 Factor a trinomial. (1 + -1n)(15 + -1n) = 0Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve: Simplifying 15 + -1n = 0 Solving 15 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1n = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1n = 0 + -15 -1n = 0 + -15 Combine like terms: 0 + -15 = -15 -1n = -15 Divide each side by '-1'. n = 15 Simplifying n = 15Solution
n = {1, 15}
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