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Simplifying (n + 4)(n + 4) = 42 Reorder the terms: (4 + n)(n + 4) = 42 Reorder the terms: (4 + n)(4 + n) = 42 Multiply (4 + n) * (4 + n) (4(4 + n) + n(4 + n)) = 42 ((4 * 4 + n * 4) + n(4 + n)) = 42 ((16 + 4n) + n(4 + n)) = 42 (16 + 4n + (4 * n + n * n)) = 42 (16 + 4n + (4n + n2)) = 42 Combine like terms: 4n + 4n = 8n (16 + 8n + n2) = 42 Solving 16 + 8n + n2 = 42 Solving for variable 'n'. Reorder the terms: 16 + -42 + 8n + n2 = 42 + -42 Combine like terms: 16 + -42 = -26 -26 + 8n + n2 = 42 + -42 Combine like terms: 42 + -42 = 0 -26 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 8n + 26 + n2 = 0 + 26 Reorder the terms: -26 + 26 + 8n + n2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 8n + n2 = 0 + 26 8n + n2 = 0 + 26 Combine like terms: 0 + 26 = 26 8n + n2 = 26 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 = 26 + 16 Reorder the terms: 16 + 8n + n2 = 26 + 16 Combine like terms: 26 + 16 = 42 16 + 8n + n2 = 42 Factor a perfect square on the left side: (n + 4)(n + 4) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (n + 4) equal to 6.480740698 and -6.480740698.Subproblem 1
n + 4 = 6.480740698 Simplifying n + 4 = 6.480740698 Reorder the terms: 4 + n = 6.480740698 Solving 4 + n = 6.480740698 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 = 6.480740698 + -4 Combine like terms: 4 + -4 = 0 0 + n = 6.480740698 + -4 n = 6.480740698 + -4 Combine like terms: 6.480740698 + -4 = 2.480740698 n = 2.480740698 Simplifying n = 2.480740698Subproblem 2
n + 4 = -6.480740698 Simplifying n + 4 = -6.480740698 Reorder the terms: 4 + n = -6.480740698 Solving 4 + n = -6.480740698 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 = -6.480740698 + -4 Combine like terms: 4 + -4 = 0 0 + n = -6.480740698 + -4 n = -6.480740698 + -4 Combine like terms: -6.480740698 + -4 = -10.480740698 n = -10.480740698 Simplifying n = -10.480740698Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.480740698, -10.480740698}
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