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Simplifying 2n2 + 20n + 40 = 2 Reorder the terms: 40 + 20n + 2n2 = 2 Solving 40 + 20n + 2n2 = 2 Solving for variable 'n'. Reorder the terms: 40 + -2 + 20n + 2n2 = 2 + -2 Combine like terms: 40 + -2 = 38 38 + 20n + 2n2 = 2 + -2 Combine like terms: 2 + -2 = 0 38 + 20n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 10n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 10n + n2)' equal to zero and attempt to solve: Simplifying 19 + 10n + n2 = 0 Solving 19 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 10n + -19 + n2 = 0 + -19 Reorder the terms: 19 + -19 + 10n + n2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 10n + n2 = 0 + -19 10n + n2 = 0 + -19 Combine like terms: 0 + -19 = -19 10n + n2 = -19 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = -19 + 25 Reorder the terms: 25 + 10n + n2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + 10n + n2 = 6 Factor a perfect square on the left side: (n + 5)(n + 5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (n + 5) equal to 2.449489743 and -2.449489743.Subproblem 1
n + 5 = 2.449489743 Simplifying n + 5 = 2.449489743 Reorder the terms: 5 + n = 2.449489743 Solving 5 + n = 2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 2.449489743 + -5 Combine like terms: 5 + -5 = 0 0 + n = 2.449489743 + -5 n = 2.449489743 + -5 Combine like terms: 2.449489743 + -5 = -2.550510257 n = -2.550510257 Simplifying n = -2.550510257Subproblem 2
n + 5 = -2.449489743 Simplifying n + 5 = -2.449489743 Reorder the terms: 5 + n = -2.449489743 Solving 5 + n = -2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -2.449489743 + -5 Combine like terms: 5 + -5 = 0 0 + n = -2.449489743 + -5 n = -2.449489743 + -5 Combine like terms: -2.449489743 + -5 = -7.449489743 n = -7.449489743 Simplifying n = -7.449489743Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.550510257, -7.449489743}Solution
n = {-2.550510257, -7.449489743}
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