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Simplifying n2 + -10n + -47 = 9 Reorder the terms: -47 + -10n + n2 = 9 Solving -47 + -10n + n2 = 9 Solving for variable 'n'. Reorder the terms: -47 + -9 + -10n + n2 = 9 + -9 Combine like terms: -47 + -9 = -56 -56 + -10n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -56 + -10n + n2 = 0 Factor a trinomial. (-4 + -1n)(14 + -1n) = 0Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve: Simplifying 14 + -1n = 0 Solving 14 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1n = 0 + -14 -1n = 0 + -14 Combine like terms: 0 + -14 = -14 -1n = -14 Divide each side by '-1'. n = 14 Simplifying n = 14Solution
n = {-4, 14}
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