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Simplifying n2 + 8n + -75 = 0 Reorder the terms: -75 + 8n + n2 = 0 Solving -75 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 8n + 75 + n2 = 0 + 75 Reorder the terms: -75 + 75 + 8n + n2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 8n + n2 = 0 + 75 8n + n2 = 0 + 75 Combine like terms: 0 + 75 = 75 8n + n2 = 75 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 = 75 + 16 Reorder the terms: 16 + 8n + n2 = 75 + 16 Combine like terms: 75 + 16 = 91 16 + 8n + n2 = 91 Factor a perfect square on the left side: (n + 4)(n + 4) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (n + 4) equal to 9.539392014 and -9.539392014.Subproblem 1
n + 4 = 9.539392014 Simplifying n + 4 = 9.539392014 Reorder the terms: 4 + n = 9.539392014 Solving 4 + n = 9.539392014 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 = 9.539392014 + -4 Combine like terms: 4 + -4 = 0 0 + n = 9.539392014 + -4 n = 9.539392014 + -4 Combine like terms: 9.539392014 + -4 = 5.539392014 n = 5.539392014 Simplifying n = 5.539392014Subproblem 2
n + 4 = -9.539392014 Simplifying n + 4 = -9.539392014 Reorder the terms: 4 + n = -9.539392014 Solving 4 + n = -9.539392014 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 = -9.539392014 + -4 Combine like terms: 4 + -4 = 0 0 + n = -9.539392014 + -4 n = -9.539392014 + -4 Combine like terms: -9.539392014 + -4 = -13.539392014 n = -13.539392014 Simplifying n = -13.539392014Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.539392014, -13.539392014}
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