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Simplifying n2 + -8n + 16 = 15 Reorder the terms: 16 + -8n + n2 = 15 Solving 16 + -8n + n2 = 15 Solving for variable 'n'. Reorder the terms: 16 + -15 + -8n + n2 = 15 + -15 Combine like terms: 16 + -15 = 1 1 + -8n + n2 = 15 + -15 Combine like terms: 15 + -15 = 0 1 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -8n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8n + n2 = 0 + -1 -8n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8n + n2 = -1 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 = -1 + 16 Reorder the terms: 16 + -8n + n2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8n + n2 = 15 Factor a perfect square on the left side: (n + -4)(n + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (n + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
n + -4 = 3.872983346 Simplifying n + -4 = 3.872983346 Reorder the terms: -4 + n = 3.872983346 Solving -4 + n = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + n = 3.872983346 + 4 n = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 n = 7.872983346 Simplifying n = 7.872983346Subproblem 2
n + -4 = -3.872983346 Simplifying n + -4 = -3.872983346 Reorder the terms: -4 + n = -3.872983346 Solving -4 + n = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + n = -3.872983346 + 4 n = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 n = 0.127016654 Simplifying n = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.872983346, 0.127016654}
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