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Simplifying 100 = n(n + 1) + 10 Reorder the terms: 100 = n(1 + n) + 10 100 = (1 * n + n * n) + 10 100 = (1n + n2) + 10 Reorder the terms: 100 = 10 + 1n + n2 Solving 100 = 10 + 1n + n2 Solving for variable 'n'. Combine like terms: 100 + -10 = 90 90 + -1n + -1n2 = 10 + 1n + n2 + -10 + -1n + -1n2 Reorder the terms: 90 + -1n + -1n2 = 10 + -10 + 1n + -1n + n2 + -1n2 Combine like terms: 10 + -10 = 0 90 + -1n + -1n2 = 0 + 1n + -1n + n2 + -1n2 90 + -1n + -1n2 = 1n + -1n + n2 + -1n2 Combine like terms: 1n + -1n = 0 90 + -1n + -1n2 = 0 + n2 + -1n2 90 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 90 + -1n + -1n2 = 0 Factor a trinomial. (9 + -1n)(10 + n) = 0Subproblem 1
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Subproblem 2
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Solution
n = {9, -10}
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