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Simplifying n2 + 7n + -72 = 0 Reorder the terms: -72 + 7n + n2 = 0 Solving -72 + 7n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 7n + 72 + n2 = 0 + 72 Reorder the terms: -72 + 72 + 7n + n2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 7n + n2 = 0 + 72 7n + n2 = 0 + 72 Combine like terms: 0 + 72 = 72 7n + n2 = 72 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 72 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 72 + 12.25 Combine like terms: 72 + 12.25 = 84.25 12.25 + 7n + n2 = 84.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (n + 3.5) equal to 9.178779875 and -9.178779875.Subproblem 1
n + 3.5 = 9.178779875 Simplifying n + 3.5 = 9.178779875 Reorder the terms: 3.5 + n = 9.178779875 Solving 3.5 + n = 9.178779875 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 9.178779875 + -3.5 n = 9.178779875 + -3.5 Combine like terms: 9.178779875 + -3.5 = 5.678779875 n = 5.678779875 Simplifying n = 5.678779875Subproblem 2
n + 3.5 = -9.178779875 Simplifying n + 3.5 = -9.178779875 Reorder the terms: 3.5 + n = -9.178779875 Solving 3.5 + n = -9.178779875 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -9.178779875 + -3.5 n = -9.178779875 + -3.5 Combine like terms: -9.178779875 + -3.5 = -12.678779875 n = -12.678779875 Simplifying n = -12.678779875Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.678779875, -12.678779875}
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