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Simplifying 306 = n(n + 1) Reorder the terms: 306 = n(1 + n) 306 = (1 * n + n * n) 306 = (1n + n2) Solving 306 = 1n + n2 Solving for variable 'n'. Reorder the terms: 306 + -1n + -1n2 = 1n + -1n + n2 + -1n2 Combine like terms: 1n + -1n = 0 306 + -1n + -1n2 = 0 + n2 + -1n2 306 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 306 + -1n + -1n2 = 0 Factor a trinomial. (17 + -1n)(18 + n) = 0Subproblem 1
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 = 17Subproblem 2
Set the factor '(18 + n)' equal to zero and attempt to solve: Simplifying 18 + n = 0 Solving 18 + n = 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 + n = 0 + -18 Combine like terms: 18 + -18 = 0 0 + n = 0 + -18 n = 0 + -18 Combine like terms: 0 + -18 = -18 n = -18 Simplifying n = -18Solution
n = {17, -18}
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