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Simplifying n2 + n + -3986 = 0 Reorder the terms: -3986 + n + n2 = 0 Solving -3986 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '3986' to each side of the equation. -3986 + n + 3986 + n2 = 0 + 3986 Reorder the terms: -3986 + 3986 + n + n2 = 0 + 3986 Combine like terms: -3986 + 3986 = 0 0 + n + n2 = 0 + 3986 n + n2 = 0 + 3986 Combine like terms: 0 + 3986 = 3986 n + n2 = 3986 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 = 3986 + 0.25 Reorder the terms: 0.25 + n + n2 = 3986 + 0.25 Combine like terms: 3986 + 0.25 = 3986.25 0.25 + n + n2 = 3986.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 3986.25 Calculate the square root of the right side: 63.136756331 Break this problem into two subproblems by setting (n + 0.5) equal to 63.136756331 and -63.136756331.Subproblem 1
n + 0.5 = 63.136756331 Simplifying n + 0.5 = 63.136756331 Reorder the terms: 0.5 + n = 63.136756331 Solving 0.5 + n = 63.136756331 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 = 63.136756331 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 63.136756331 + -0.5 n = 63.136756331 + -0.5 Combine like terms: 63.136756331 + -0.5 = 62.636756331 n = 62.636756331 Simplifying n = 62.636756331Subproblem 2
n + 0.5 = -63.136756331 Simplifying n + 0.5 = -63.136756331 Reorder the terms: 0.5 + n = -63.136756331 Solving 0.5 + n = -63.136756331 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 = -63.136756331 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -63.136756331 + -0.5 n = -63.136756331 + -0.5 Combine like terms: -63.136756331 + -0.5 = -63.636756331 n = -63.636756331 Simplifying n = -63.636756331Solution
The solution to the problem is based on the solutions from the subproblems. n = {62.636756331, -63.636756331}
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