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Simplifying 2n2 + 20n + -28 = 0 Reorder the terms: -28 + 20n + 2n2 = 0 Solving -28 + 20n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 10n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 10n + n2)' equal to zero and attempt to solve: Simplifying -14 + 10n + n2 = 0 Solving -14 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 10n + 14 + n2 = 0 + 14 Reorder the terms: -14 + 14 + 10n + n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 10n + n2 = 0 + 14 10n + n2 = 0 + 14 Combine like terms: 0 + 14 = 14 10n + n2 = 14 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 = 14 + 25 Reorder the terms: 25 + 10n + n2 = 14 + 25 Combine like terms: 14 + 25 = 39 25 + 10n + n2 = 39 Factor a perfect square on the left side: (n + 5)(n + 5) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (n + 5) equal to 6.244997998 and -6.244997998.Subproblem 1
n + 5 = 6.244997998 Simplifying n + 5 = 6.244997998 Reorder the terms: 5 + n = 6.244997998 Solving 5 + n = 6.244997998 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 = 6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + n = 6.244997998 + -5 n = 6.244997998 + -5 Combine like terms: 6.244997998 + -5 = 1.244997998 n = 1.244997998 Simplifying n = 1.244997998Subproblem 2
n + 5 = -6.244997998 Simplifying n + 5 = -6.244997998 Reorder the terms: 5 + n = -6.244997998 Solving 5 + n = -6.244997998 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 = -6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + n = -6.244997998 + -5 n = -6.244997998 + -5 Combine like terms: -6.244997998 + -5 = -11.244997998 n = -11.244997998 Simplifying n = -11.244997998Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.244997998, -11.244997998}Solution
n = {1.244997998, -11.244997998}
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