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Simplifying n2 + -1n + -584 = 0 Reorder the terms: -584 + -1n + n2 = 0 Solving -584 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '584' to each side of the equation. -584 + -1n + 584 + n2 = 0 + 584 Reorder the terms: -584 + 584 + -1n + n2 = 0 + 584 Combine like terms: -584 + 584 = 0 0 + -1n + n2 = 0 + 584 -1n + n2 = 0 + 584 Combine like terms: 0 + 584 = 584 -1n + n2 = 584 The n term is -1n. 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. -1n + 0.25 + n2 = 584 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 584 + 0.25 Combine like terms: 584 + 0.25 = 584.25 0.25 + -1n + n2 = 584.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 584.25 Calculate the square root of the right side: 24.171263931 Break this problem into two subproblems by setting (n + -0.5) equal to 24.171263931 and -24.171263931.Subproblem 1
n + -0.5 = 24.171263931 Simplifying n + -0.5 = 24.171263931 Reorder the terms: -0.5 + n = 24.171263931 Solving -0.5 + n = 24.171263931 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 = 24.171263931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 24.171263931 + 0.5 n = 24.171263931 + 0.5 Combine like terms: 24.171263931 + 0.5 = 24.671263931 n = 24.671263931 Simplifying n = 24.671263931Subproblem 2
n + -0.5 = -24.171263931 Simplifying n + -0.5 = -24.171263931 Reorder the terms: -0.5 + n = -24.171263931 Solving -0.5 + n = -24.171263931 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 = -24.171263931 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -24.171263931 + 0.5 n = -24.171263931 + 0.5 Combine like terms: -24.171263931 + 0.5 = -23.671263931 n = -23.671263931 Simplifying n = -23.671263931Solution
The solution to the problem is based on the solutions from the subproblems. n = {24.671263931, -23.671263931}
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