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Simplifying n2 = 7n + 8 Reorder the terms: n2 = 8 + 7n Solving n2 = 8 + 7n Solving for variable 'n'. Reorder the terms: -8 + -7n + n2 = 8 + 7n + -8 + -7n Reorder the terms: -8 + -7n + n2 = 8 + -8 + 7n + -7n Combine like terms: 8 + -8 = 0 -8 + -7n + n2 = 0 + 7n + -7n -8 + -7n + n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -8 + -7n + n2 = 0 Factor a trinomial. (-1 + -1n)(8 + -1n) = 0Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-1, 8}
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