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Simplifying 46n2 + 101n + 40 = -4n2 + -4n Reorder the terms: 40 + 101n + 46n2 = -4n2 + -4n Reorder the terms: 40 + 101n + 46n2 = -4n + -4n2 Solving 40 + 101n + 46n2 = -4n + -4n2 Solving for variable 'n'. Reorder the terms: 40 + 101n + 4n + 46n2 + 4n2 = -4n + -4n2 + 4n + 4n2 Combine like terms: 101n + 4n = 105n 40 + 105n + 46n2 + 4n2 = -4n + -4n2 + 4n + 4n2 Combine like terms: 46n2 + 4n2 = 50n2 40 + 105n + 50n2 = -4n + -4n2 + 4n + 4n2 Reorder the terms: 40 + 105n + 50n2 = -4n + 4n + -4n2 + 4n2 Combine like terms: -4n + 4n = 0 40 + 105n + 50n2 = 0 + -4n2 + 4n2 40 + 105n + 50n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 40 + 105n + 50n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + 21n + 10n2) = 0 Factor a trinomial. 5((8 + 5n)(1 + 2n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + 5n)' equal to zero and attempt to solve: Simplifying 8 + 5n = 0 Solving 8 + 5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5n = 0 + -8 5n = 0 + -8 Combine like terms: 0 + -8 = -8 5n = -8 Divide each side by '5'. n = -1.6 Simplifying n = -1.6Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 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 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5Solution
n = {-1.6, -0.5}
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