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Simplifying (n)(n + -1) = 870 Reorder the terms: n(-1 + n) = 870 (-1 * n + n * n) = 870 (-1n + n2) = 870 Solving -1n + n2 = 870 Solving for variable 'n'. Reorder the terms: -870 + -1n + n2 = 870 + -870 Combine like terms: 870 + -870 = 0 -870 + -1n + n2 = 0 Factor a trinomial. (-29 + -1n)(30 + -1n) = 0Subproblem 1
Set the factor '(-29 + -1n)' equal to zero and attempt to solve: Simplifying -29 + -1n = 0 Solving -29 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + -1n = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1n = 0 + 29 -1n = 0 + 29 Combine like terms: 0 + 29 = 29 -1n = 29 Divide each side by '-1'. n = -29 Simplifying n = -29Subproblem 2
Set the factor '(30 + -1n)' equal to zero and attempt to solve: Simplifying 30 + -1n = 0 Solving 30 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1n = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1n = 0 + -30 -1n = 0 + -30 Combine like terms: 0 + -30 = -30 -1n = -30 Divide each side by '-1'. n = 30 Simplifying n = 30Solution
n = {-29, 30}
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