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Simplifying n2 + -8n + 16 = 6 Reorder the terms: 16 + -8n + n2 = 6 Solving 16 + -8n + n2 = 6 Solving for variable 'n'. Reorder the terms: 16 + -6 + -8n + n2 = 6 + -6 Combine like terms: 16 + -6 = 10 10 + -8n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 10 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8n + -10 + n2 = 0 + -10 Reorder the terms: 10 + -10 + -8n + n2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8n + n2 = 0 + -10 -8n + n2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8n + n2 = -10 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 = -10 + 16 Reorder the terms: 16 + -8n + n2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8n + n2 = 6 Factor a perfect square on the left side: (n + -4)(n + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (n + -4) equal to 2.449489743 and -2.449489743.Subproblem 1
n + -4 = 2.449489743 Simplifying n + -4 = 2.449489743 Reorder the terms: -4 + n = 2.449489743 Solving -4 + n = 2.449489743 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 = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + n = 2.449489743 + 4 n = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 n = 6.449489743 Simplifying n = 6.449489743Subproblem 2
n + -4 = -2.449489743 Simplifying n + -4 = -2.449489743 Reorder the terms: -4 + n = -2.449489743 Solving -4 + n = -2.449489743 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 = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + n = -2.449489743 + 4 n = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 n = 1.550510257 Simplifying n = 1.550510257Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.449489743, 1.550510257}
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