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Simplifying n2 = -45 + 14n Solving n2 = -45 + 14n Solving for variable 'n'. Reorder the terms: 45 + -14n + n2 = -45 + 14n + 45 + -14n Reorder the terms: 45 + -14n + n2 = -45 + 45 + 14n + -14n Combine like terms: -45 + 45 = 0 45 + -14n + n2 = 0 + 14n + -14n 45 + -14n + n2 = 14n + -14n Combine like terms: 14n + -14n = 0 45 + -14n + n2 = 0 Factor a trinomial. (5 + -1n)(9 + -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 '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {5, 9}
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