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Simplifying (10n + 5)(10n + 5) = 0 Reorder the terms: (5 + 10n)(10n + 5) = 0 Reorder the terms: (5 + 10n)(5 + 10n) = 0 Multiply (5 + 10n) * (5 + 10n) (5(5 + 10n) + 10n * (5 + 10n)) = 0 ((5 * 5 + 10n * 5) + 10n * (5 + 10n)) = 0 ((25 + 50n) + 10n * (5 + 10n)) = 0 (25 + 50n + (5 * 10n + 10n * 10n)) = 0 (25 + 50n + (50n + 100n2)) = 0 Combine like terms: 50n + 50n = 100n (25 + 100n + 100n2) = 0 Solving 25 + 100n + 100n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '25'. 25(1 + 4n + 4n2) = 0 Factor a trinomial. 25((1 + 2n)(1 + 2n)) = 0 Ignore the factor 25.Subproblem 1
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 = -0.5Subproblem 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 = {-0.5, -0.5}
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