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Simplifying 98n2 + 301n + 145 = 5 Reorder the terms: 145 + 301n + 98n2 = 5 Solving 145 + 301n + 98n2 = 5 Solving for variable 'n'. Reorder the terms: 145 + -5 + 301n + 98n2 = 5 + -5 Combine like terms: 145 + -5 = 140 140 + 301n + 98n2 = 5 + -5 Combine like terms: 5 + -5 = 0 140 + 301n + 98n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(20 + 43n + 14n2) = 0 Factor a trinomial. 7((5 + 2n)(4 + 7n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + 2n)' equal to zero and attempt to solve: Simplifying 5 + 2n = 0 Solving 5 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2n = 0 + -5 2n = 0 + -5 Combine like terms: 0 + -5 = -5 2n = -5 Divide each side by '2'. n = -2.5 Simplifying n = -2.5Subproblem 2
Set the factor '(4 + 7n)' equal to zero and attempt to solve: Simplifying 4 + 7n = 0 Solving 4 + 7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7n = 0 + -4 7n = 0 + -4 Combine like terms: 0 + -4 = -4 7n = -4 Divide each side by '7'. n = -0.5714285714 Simplifying n = -0.5714285714Solution
n = {-2.5, -0.5714285714}
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