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Simplifying 0 = -1n2 + 490n + -39000 Reorder the terms: 0 = -39000 + 490n + -1n2 Solving 0 = -39000 + 490n + -1n2 Solving for variable 'n'. Combine like terms: 0 + 39000 = 39000 39000 + -490n + n2 = -39000 + 490n + -1n2 + 39000 + -490n + n2 Reorder the terms: 39000 + -490n + n2 = -39000 + 39000 + 490n + -490n + -1n2 + n2 Combine like terms: -39000 + 39000 = 0 39000 + -490n + n2 = 0 + 490n + -490n + -1n2 + n2 39000 + -490n + n2 = 490n + -490n + -1n2 + n2 Combine like terms: 490n + -490n = 0 39000 + -490n + n2 = 0 + -1n2 + n2 39000 + -490n + n2 = -1n2 + n2 Combine like terms: -1n2 + n2 = 0 39000 + -490n + n2 = 0 Factor a trinomial. (100 + -1n)(390 + -1n) = 0Subproblem 1
Set the factor '(100 + -1n)' equal to zero and attempt to solve: Simplifying 100 + -1n = 0 Solving 100 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1n = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1n = 0 + -100 -1n = 0 + -100 Combine like terms: 0 + -100 = -100 -1n = -100 Divide each side by '-1'. n = 100 Simplifying n = 100Subproblem 2
Set the factor '(390 + -1n)' equal to zero and attempt to solve: Simplifying 390 + -1n = 0 Solving 390 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-390' to each side of the equation. 390 + -390 + -1n = 0 + -390 Combine like terms: 390 + -390 = 0 0 + -1n = 0 + -390 -1n = 0 + -390 Combine like terms: 0 + -390 = -390 -1n = -390 Divide each side by '-1'. n = 390 Simplifying n = 390Solution
n = {100, 390}
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