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Simplifying 342 = n2 + n Reorder the terms: 342 = n + n2 Solving 342 = n + n2 Solving for variable 'n'. Reorder the terms: 342 + -1n + -1n2 = n + -1n + n2 + -1n2 Combine like terms: n + -1n = 0 342 + -1n + -1n2 = 0 + n2 + -1n2 342 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 342 + -1n + -1n2 = 0 Factor a trinomial. (18 + -1n)(19 + n) = 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 '(19 + n)' equal to zero and attempt to solve: Simplifying 19 + n = 0 Solving 19 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + n = 0 + -19 Combine like terms: 19 + -19 = 0 0 + n = 0 + -19 n = 0 + -19 Combine like terms: 0 + -19 = -19 n = -19 Simplifying n = -19Solution
n = {18, -19}
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