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Simplifying n2 + 8n + -14 = 0 Reorder the terms: -14 + 8n + n2 = 0 Solving -14 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 8n + 14 + n2 = 0 + 14 Reorder the terms: -14 + 14 + 8n + n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8n + n2 = 0 + 14 8n + n2 = 0 + 14 Combine like terms: 0 + 14 = 14 8n + n2 = 14 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = 14 + 16 Reorder the terms: 16 + 8n + n2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8n + n2 = 30 Factor a perfect square on the left side: (n + 4)(n + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (n + 4) equal to 5.477225575 and -5.477225575.Subproblem 1
n + 4 = 5.477225575 Simplifying n + 4 = 5.477225575 Reorder the terms: 4 + n = 5.477225575 Solving 4 + n = 5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + n = 5.477225575 + -4 n = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 n = 1.477225575 Simplifying n = 1.477225575Subproblem 2
n + 4 = -5.477225575 Simplifying n + 4 = -5.477225575 Reorder the terms: 4 + n = -5.477225575 Solving 4 + n = -5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + n = -5.477225575 + -4 n = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 n = -9.477225575 Simplifying n = -9.477225575Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.477225575, -9.477225575}
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