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Simplifying n2 = 2n + 8 Reorder the terms: n2 = 8 + 2n Solving n2 = 8 + 2n Solving for variable 'n'. Reorder the terms: -8 + -2n + n2 = 8 + 2n + -8 + -2n Reorder the terms: -8 + -2n + n2 = 8 + -8 + 2n + -2n Combine like terms: 8 + -8 = 0 -8 + -2n + n2 = 0 + 2n + -2n -8 + -2n + n2 = 2n + -2n Combine like terms: 2n + -2n = 0 -8 + -2n + n2 = 0 Factor a trinomial. (-2 + -1n)(4 + -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 '(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 = {-2, 4}
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