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Simplifying 25n2 + 4n + -1 = 1 + -5n2 Reorder the terms: -1 + 4n + 25n2 = 1 + -5n2 Solving -1 + 4n + 25n2 = 1 + -5n2 Solving for variable 'n'. Reorder the terms: -1 + -1 + 4n + 25n2 + 5n2 = 1 + -5n2 + -1 + 5n2 Combine like terms: -1 + -1 = -2 -2 + 4n + 25n2 + 5n2 = 1 + -5n2 + -1 + 5n2 Combine like terms: 25n2 + 5n2 = 30n2 -2 + 4n + 30n2 = 1 + -5n2 + -1 + 5n2 Reorder the terms: -2 + 4n + 30n2 = 1 + -1 + -5n2 + 5n2 Combine like terms: 1 + -1 = 0 -2 + 4n + 30n2 = 0 + -5n2 + 5n2 -2 + 4n + 30n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 -2 + 4n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2n + 15n2) = 0 Factor a trinomial. 2((-1 + -3n)(1 + -5n)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve: Simplifying 1 + -5n = 0 Solving 1 + -5n = 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 + -5n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5n = 0 + -1 -5n = 0 + -1 Combine like terms: 0 + -1 = -1 -5n = -1 Divide each side by '-5'. n = 0.2 Simplifying n = 0.2Solution
n = {-0.3333333333, 0.2}
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