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Simplifying 182 = n2 + n Reorder the terms: 182 = n + n2 Solving 182 = n + n2 Solving for variable 'n'. Reorder the terms: 182 + -1n + -1n2 = n + -1n + n2 + -1n2 Combine like terms: n + -1n = 0 182 + -1n + -1n2 = 0 + n2 + -1n2 182 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 182 + -1n + -1n2 = 0 Factor a trinomial. (13 + -1n)(14 + n) = 0Subproblem 1
Set the factor '(13 + -1n)' equal to zero and attempt to solve: Simplifying 13 + -1n = 0 Solving 13 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1n = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1n = 0 + -13 -1n = 0 + -13 Combine like terms: 0 + -13 = -13 -1n = -13 Divide each side by '-1'. n = 13 Simplifying n = 13Subproblem 2
Set the factor '(14 + n)' equal to zero and attempt to solve: Simplifying 14 + n = 0 Solving 14 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + n = 0 + -14 n = 0 + -14 Combine like terms: 0 + -14 = -14 n = -14 Simplifying n = -14Solution
n = {13, -14}
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