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Simplifying 8n2 + 16n + -40 = 0 Reorder the terms: -40 + 16n + 8n2 = 0 Solving -40 + 16n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 2n + n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + 2n + n2)' equal to zero and attempt to solve: Simplifying -5 + 2n + n2 = 0 Solving -5 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + 2n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2n + n2 = 0 + 5 2n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 2n + n2 = 5 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 5 + 1 Reorder the terms: 1 + 2n + n2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2n + n2 = 6 Factor a perfect square on the left side: (n + 1)(n + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (n + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
n + 1 = 2.449489743 Simplifying n + 1 = 2.449489743 Reorder the terms: 1 + n = 2.449489743 Solving 1 + n = 2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.449489743 + -1 n = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 n = 1.449489743 Simplifying n = 1.449489743Subproblem 2
n + 1 = -2.449489743 Simplifying n + 1 = -2.449489743 Reorder the terms: 1 + n = -2.449489743 Solving 1 + n = -2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.449489743 + -1 n = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 n = -3.449489743 Simplifying n = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.449489743, -3.449489743}Solution
n = {1.449489743, -3.449489743}
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