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Simplifying n2 + 8n + -34 = 2 Reorder the terms: -34 + 8n + n2 = 2 Solving -34 + 8n + n2 = 2 Solving for variable 'n'. Reorder the terms: -34 + -2 + 8n + n2 = 2 + -2 Combine like terms: -34 + -2 = -36 -36 + 8n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -36 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 8n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + 8n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 8n + n2 = 0 + 36 8n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 8n + n2 = 36 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 = 36 + 16 Reorder the terms: 16 + 8n + n2 = 36 + 16 Combine like terms: 36 + 16 = 52 16 + 8n + n2 = 52 Factor a perfect square on the left side: (n + 4)(n + 4) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (n + 4) equal to 7.211102551 and -7.211102551.Subproblem 1
n + 4 = 7.211102551 Simplifying n + 4 = 7.211102551 Reorder the terms: 4 + n = 7.211102551 Solving 4 + n = 7.211102551 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 = 7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + n = 7.211102551 + -4 n = 7.211102551 + -4 Combine like terms: 7.211102551 + -4 = 3.211102551 n = 3.211102551 Simplifying n = 3.211102551Subproblem 2
n + 4 = -7.211102551 Simplifying n + 4 = -7.211102551 Reorder the terms: 4 + n = -7.211102551 Solving 4 + n = -7.211102551 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 = -7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + n = -7.211102551 + -4 n = -7.211102551 + -4 Combine like terms: -7.211102551 + -4 = -11.211102551 n = -11.211102551 Simplifying n = -11.211102551Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.211102551, -11.211102551}
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