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Simplifying n2 + 7n + -250 = 0 Reorder the terms: -250 + 7n + n2 = 0 Solving -250 + 7n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 7n + 250 + n2 = 0 + 250 Reorder the terms: -250 + 250 + 7n + n2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 7n + n2 = 0 + 250 7n + n2 = 0 + 250 Combine like terms: 0 + 250 = 250 7n + n2 = 250 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 = 250 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 250 + 12.25 Combine like terms: 250 + 12.25 = 262.25 12.25 + 7n + n2 = 262.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 262.25 Calculate the square root of the right side: 16.194134741 Break this problem into two subproblems by setting (n + 3.5) equal to 16.194134741 and -16.194134741.Subproblem 1
n + 3.5 = 16.194134741 Simplifying n + 3.5 = 16.194134741 Reorder the terms: 3.5 + n = 16.194134741 Solving 3.5 + n = 16.194134741 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 = 16.194134741 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 16.194134741 + -3.5 n = 16.194134741 + -3.5 Combine like terms: 16.194134741 + -3.5 = 12.694134741 n = 12.694134741 Simplifying n = 12.694134741Subproblem 2
n + 3.5 = -16.194134741 Simplifying n + 3.5 = -16.194134741 Reorder the terms: 3.5 + n = -16.194134741 Solving 3.5 + n = -16.194134741 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 = -16.194134741 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -16.194134741 + -3.5 n = -16.194134741 + -3.5 Combine like terms: -16.194134741 + -3.5 = -19.694134741 n = -19.694134741 Simplifying n = -19.694134741Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.694134741, -19.694134741}
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