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Simplifying n2 + -4n + 11 = 56 Reorder the terms: 11 + -4n + n2 = 56 Solving 11 + -4n + n2 = 56 Solving for variable 'n'. Reorder the terms: 11 + -56 + -4n + n2 = 56 + -56 Combine like terms: 11 + -56 = -45 -45 + -4n + n2 = 56 + -56 Combine like terms: 56 + -56 = 0 -45 + -4n + 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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