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Simplifying n2 + n + -400 = 0 Reorder the terms: -400 + n + n2 = 0 Solving -400 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + n + 400 + n2 = 0 + 400 Reorder the terms: -400 + 400 + n + n2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + n + n2 = 0 + 400 n + n2 = 0 + 400 Combine like terms: 0 + 400 = 400 n + n2 = 400 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 = 400 + 0.25 Reorder the terms: 0.25 + n + n2 = 400 + 0.25 Combine like terms: 400 + 0.25 = 400.25 0.25 + n + n2 = 400.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (n + 0.5) equal to 20.006249024 and -20.006249024.Subproblem 1
n + 0.5 = 20.006249024 Simplifying n + 0.5 = 20.006249024 Reorder the terms: 0.5 + n = 20.006249024 Solving 0.5 + n = 20.006249024 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 = 20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 20.006249024 + -0.5 n = 20.006249024 + -0.5 Combine like terms: 20.006249024 + -0.5 = 19.506249024 n = 19.506249024 Simplifying n = 19.506249024Subproblem 2
n + 0.5 = -20.006249024 Simplifying n + 0.5 = -20.006249024 Reorder the terms: 0.5 + n = -20.006249024 Solving 0.5 + n = -20.006249024 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 = -20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -20.006249024 + -0.5 n = -20.006249024 + -0.5 Combine like terms: -20.006249024 + -0.5 = -20.506249024 n = -20.506249024 Simplifying n = -20.506249024Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.506249024, -20.506249024}
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