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Simplifying n2 + -4n + -41 = -8 Reorder the terms: -41 + -4n + n2 = -8 Solving -41 + -4n + n2 = -8 Solving for variable 'n'. Reorder the terms: -41 + 8 + -4n + n2 = -8 + 8 Combine like terms: -41 + 8 = -33 -33 + -4n + n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -33 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -4n + 33 + n2 = 0 + 33 Reorder the terms: -33 + 33 + -4n + n2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -4n + n2 = 0 + 33 -4n + n2 = 0 + 33 Combine like terms: 0 + 33 = 33 -4n + n2 = 33 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 33 + 4 Reorder the terms: 4 + -4n + n2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + -4n + n2 = 37 Factor a perfect square on the left side: (n + -2)(n + -2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (n + -2) equal to 6.08276253 and -6.08276253.Subproblem 1
n + -2 = 6.08276253 Simplifying n + -2 = 6.08276253 Reorder the terms: -2 + n = 6.08276253 Solving -2 + n = 6.08276253 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + n = 6.08276253 + 2 n = 6.08276253 + 2 Combine like terms: 6.08276253 + 2 = 8.08276253 n = 8.08276253 Simplifying n = 8.08276253Subproblem 2
n + -2 = -6.08276253 Simplifying n + -2 = -6.08276253 Reorder the terms: -2 + n = -6.08276253 Solving -2 + n = -6.08276253 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + n = -6.08276253 + 2 n = -6.08276253 + 2 Combine like terms: -6.08276253 + 2 = -4.08276253 n = -4.08276253 Simplifying n = -4.08276253Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.08276253, -4.08276253}
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