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Simplifying n2 + 4n + -17 = 0 Reorder the terms: -17 + 4n + n2 = 0 Solving -17 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 4n + 17 + n2 = 0 + 17 Reorder the terms: -17 + 17 + 4n + n2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 4n + n2 = 0 + 17 4n + n2 = 0 + 17 Combine like terms: 0 + 17 = 17 4n + n2 = 17 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 = 17 + 4 Reorder the terms: 4 + 4n + n2 = 17 + 4 Combine like terms: 17 + 4 = 21 4 + 4n + n2 = 21 Factor a perfect square on the left side: (n + 2)(n + 2) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (n + 2) equal to 4.582575695 and -4.582575695.Subproblem 1
n + 2 = 4.582575695 Simplifying n + 2 = 4.582575695 Reorder the terms: 2 + n = 4.582575695 Solving 2 + n = 4.582575695 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 = 4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.582575695 + -2 n = 4.582575695 + -2 Combine like terms: 4.582575695 + -2 = 2.582575695 n = 2.582575695 Simplifying n = 2.582575695Subproblem 2
n + 2 = -4.582575695 Simplifying n + 2 = -4.582575695 Reorder the terms: 2 + n = -4.582575695 Solving 2 + n = -4.582575695 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 = -4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.582575695 + -2 n = -4.582575695 + -2 Combine like terms: -4.582575695 + -2 = -6.582575695 n = -6.582575695 Simplifying n = -6.582575695Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.582575695, -6.582575695}
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