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Simplifying n2 + 9n + 17 = n + 2 Reorder the terms: 17 + 9n + n2 = n + 2 Reorder the terms: 17 + 9n + n2 = 2 + n Solving 17 + 9n + n2 = 2 + n Solving for variable 'n'. Reorder the terms: 17 + -2 + 9n + -1n + n2 = 2 + n + -2 + -1n Combine like terms: 17 + -2 = 15 15 + 9n + -1n + n2 = 2 + n + -2 + -1n Combine like terms: 9n + -1n = 8n 15 + 8n + n2 = 2 + n + -2 + -1n Reorder the terms: 15 + 8n + n2 = 2 + -2 + n + -1n Combine like terms: 2 + -2 = 0 15 + 8n + n2 = 0 + n + -1n 15 + 8n + n2 = n + -1n Combine like terms: n + -1n = 0 15 + 8n + n2 = 0 Factor a trinomial. (5 + n)(3 + n) = 0Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 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 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve: Simplifying 3 + n = 0 Solving 3 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + n = 0 + -3 n = 0 + -3 Combine like terms: 0 + -3 = -3 n = -3 Simplifying n = -3Solution
n = {-5, -3}
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