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Simplifying -2n2 + -8n + -2 = 0 Reorder the terms: -2 + -8n + -2n2 = 0 Solving -2 + -8n + -2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 4n + n2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 4n + n2)' equal to zero and attempt to solve: Simplifying 1 + 4n + n2 = 0 Solving 1 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + 4n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4n + n2 = 0 + -1 4n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 4n + n2 = -1 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = -1 + 4 Reorder the terms: 4 + 4n + n2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4n + n2 = 3 Factor a perfect square on the left side: (n + 2)(n + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (n + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
n + 2 = 1.732050808 Simplifying n + 2 = 1.732050808 Reorder the terms: 2 + n = 1.732050808 Solving 2 + n = 1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + n = 1.732050808 + -2 n = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 n = -0.267949192 Simplifying n = -0.267949192Subproblem 2
n + 2 = -1.732050808 Simplifying n + 2 = -1.732050808 Reorder the terms: 2 + n = -1.732050808 Solving 2 + n = -1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + n = -1.732050808 + -2 n = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 n = -3.732050808 Simplifying n = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.267949192, -3.732050808}Solution
n = {-0.267949192, -3.732050808}
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