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Simplifying 2n2 + n + -558 = 0 Reorder the terms: -558 + n + 2n2 = 0 Solving -558 + n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -279 + 0.5n + n2 = 0 Move the constant term to the right: Add '279' to each side of the equation. -279 + 0.5n + 279 + n2 = 0 + 279 Reorder the terms: -279 + 279 + 0.5n + n2 = 0 + 279 Combine like terms: -279 + 279 = 0 0 + 0.5n + n2 = 0 + 279 0.5n + n2 = 0 + 279 Combine like terms: 0 + 279 = 279 0.5n + n2 = 279 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. 0.5n + 0.25 + n2 = 279 + 0.25 Reorder the terms: 0.25 + 0.5n + n2 = 279 + 0.25 Combine like terms: 279 + 0.25 = 279.25 0.25 + 0.5n + n2 = 279.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 279.25 Calculate the square root of the right side: 16.710774967 Break this problem into two subproblems by setting (n + 0.5) equal to 16.710774967 and -16.710774967.Subproblem 1
n + 0.5 = 16.710774967 Simplifying n + 0.5 = 16.710774967 Reorder the terms: 0.5 + n = 16.710774967 Solving 0.5 + n = 16.710774967 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 = 16.710774967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 16.710774967 + -0.5 n = 16.710774967 + -0.5 Combine like terms: 16.710774967 + -0.5 = 16.210774967 n = 16.210774967 Simplifying n = 16.210774967Subproblem 2
n + 0.5 = -16.710774967 Simplifying n + 0.5 = -16.710774967 Reorder the terms: 0.5 + n = -16.710774967 Solving 0.5 + n = -16.710774967 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 = -16.710774967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -16.710774967 + -0.5 n = -16.710774967 + -0.5 Combine like terms: -16.710774967 + -0.5 = -17.210774967 n = -17.210774967 Simplifying n = -17.210774967Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.210774967, -17.210774967}
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