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Simplifying n2 + n = 50 Reorder the terms: n + n2 = 50 Solving n + n2 = 50 Solving for variable 'n'. Reorder the terms: -50 + n + n2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + n + 50 + n2 = 0 + 50 Reorder the terms: -50 + 50 + n + n2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + n + n2 = 0 + 50 n + n2 = 0 + 50 Combine like terms: 0 + 50 = 50 n + n2 = 50 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 50 + 0.25 Reorder the terms: 0.25 + n + n2 = 50 + 0.25 Combine like terms: 50 + 0.25 = 50.25 0.25 + n + n2 = 50.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (n + 0.5) equal to 7.088723439 and -7.088723439.Subproblem 1
n + 0.5 = 7.088723439 Simplifying n + 0.5 = 7.088723439 Reorder the terms: 0.5 + n = 7.088723439 Solving 0.5 + n = 7.088723439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 7.088723439 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 7.088723439 + -0.5 n = 7.088723439 + -0.5 Combine like terms: 7.088723439 + -0.5 = 6.588723439 n = 6.588723439 Simplifying n = 6.588723439Subproblem 2
n + 0.5 = -7.088723439 Simplifying n + 0.5 = -7.088723439 Reorder the terms: 0.5 + n = -7.088723439 Solving 0.5 + n = -7.088723439 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -7.088723439 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -7.088723439 + -0.5 n = -7.088723439 + -0.5 Combine like terms: -7.088723439 + -0.5 = -7.588723439 n = -7.588723439 Simplifying n = -7.588723439Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.588723439, -7.588723439}
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