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Simplifying 18n2 + -3n = 1 Reorder the terms: -3n + 18n2 = 1 Solving -3n + 18n2 = 1 Solving for variable 'n'. Reorder the terms: -1 + -3n + 18n2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -3n + 18n2 = 0 Factor a trinomial. (-1 + -6n)(1 + -3n) = 0Subproblem 1
Set the factor '(-1 + -6n)' equal to zero and attempt to solve: Simplifying -1 + -6n = 0 Solving -1 + -6n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -6n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6n = 0 + 1 -6n = 0 + 1 Combine like terms: 0 + 1 = 1 -6n = 1 Divide each side by '-6'. n = -0.1666666667 Simplifying n = -0.1666666667Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-0.1666666667, 0.3333333333}
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