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Simplifying n2 + n + -1378 = 0 Reorder the terms: -1378 + n + n2 = 0 Solving -1378 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1378' to each side of the equation. -1378 + n + 1378 + n2 = 0 + 1378 Reorder the terms: -1378 + 1378 + n + n2 = 0 + 1378 Combine like terms: -1378 + 1378 = 0 0 + n + n2 = 0 + 1378 n + n2 = 0 + 1378 Combine like terms: 0 + 1378 = 1378 n + n2 = 1378 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 = 1378 + 0.25 Reorder the terms: 0.25 + n + n2 = 1378 + 0.25 Combine like terms: 1378 + 0.25 = 1378.25 0.25 + n + n2 = 1378.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1378.25 Calculate the square root of the right side: 37.124789562 Break this problem into two subproblems by setting (n + 0.5) equal to 37.124789562 and -37.124789562.Subproblem 1
n + 0.5 = 37.124789562 Simplifying n + 0.5 = 37.124789562 Reorder the terms: 0.5 + n = 37.124789562 Solving 0.5 + n = 37.124789562 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 = 37.124789562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 37.124789562 + -0.5 n = 37.124789562 + -0.5 Combine like terms: 37.124789562 + -0.5 = 36.624789562 n = 36.624789562 Simplifying n = 36.624789562Subproblem 2
n + 0.5 = -37.124789562 Simplifying n + 0.5 = -37.124789562 Reorder the terms: 0.5 + n = -37.124789562 Solving 0.5 + n = -37.124789562 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 = -37.124789562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -37.124789562 + -0.5 n = -37.124789562 + -0.5 Combine like terms: -37.124789562 + -0.5 = -37.624789562 n = -37.624789562 Simplifying n = -37.624789562Solution
The solution to the problem is based on the solutions from the subproblems. n = {36.624789562, -37.624789562}
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