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Simplifying n(n + 1) = 306 Reorder the terms: n(1 + n) = 306 (1 * n + n * n) = 306 (1n + n2) = 306 Solving 1n + n2 = 306 Solving for variable 'n'. Reorder the terms: -306 + 1n + n2 = 306 + -306 Combine like terms: 306 + -306 = 0 -306 + 1n + n2 = 0 Factor a trinomial. (-18 + -1n)(17 + -1n) = 0Subproblem 1
Set the factor '(-18 + -1n)' equal to zero and attempt to solve: Simplifying -18 + -1n = 0 Solving -18 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1n = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1n = 0 + 18 -1n = 0 + 18 Combine like terms: 0 + 18 = 18 -1n = 18 Divide each side by '-1'. n = -18 Simplifying n = -18Subproblem 2
Set the factor '(17 + -1n)' equal to zero and attempt to solve: Simplifying 17 + -1n = 0 Solving 17 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1n = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1n = 0 + -17 -1n = 0 + -17 Combine like terms: 0 + -17 = -17 -1n = -17 Divide each side by '-1'. n = 17 Simplifying n = 17Solution
n = {-18, 17}
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