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Simplifying 3n2 + 10n + -77 = 11 Reorder the terms: -77 + 10n + 3n2 = 11 Solving -77 + 10n + 3n2 = 11 Solving for variable 'n'. Reorder the terms: -77 + -11 + 10n + 3n2 = 11 + -11 Combine like terms: -77 + -11 = -88 -88 + 10n + 3n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -88 + 10n + 3n2 = 0 Factor a trinomial. (-22 + -3n)(4 + -1n) = 0Subproblem 1
Set the factor '(-22 + -3n)' equal to zero and attempt to solve: Simplifying -22 + -3n = 0 Solving -22 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -3n = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -3n = 0 + 22 -3n = 0 + 22 Combine like terms: 0 + 22 = 22 -3n = 22 Divide each side by '-3'. n = -7.333333333 Simplifying n = -7.333333333Subproblem 2
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 = 4Solution
n = {-7.333333333, 4}
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