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Simplifying n2 + -18n + -31 = 9 Reorder the terms: -31 + -18n + n2 = 9 Solving -31 + -18n + n2 = 9 Solving for variable 'n'. Reorder the terms: -31 + -9 + -18n + n2 = 9 + -9 Combine like terms: -31 + -9 = -40 -40 + -18n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -40 + -18n + n2 = 0 Factor a trinomial. (-2 + -1n)(20 + -1n) = 0Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve: Simplifying 20 + -1n = 0 Solving 20 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1n = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1n = 0 + -20 -1n = 0 + -20 Combine like terms: 0 + -20 = -20 -1n = -20 Divide each side by '-1'. n = 20 Simplifying n = 20Solution
n = {-2, 20}
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