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Simplifying n2 + -1n + -323 = 0 Reorder the terms: -323 + -1n + n2 = 0 Solving -323 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '323' to each side of the equation. -323 + -1n + 323 + n2 = 0 + 323 Reorder the terms: -323 + 323 + -1n + n2 = 0 + 323 Combine like terms: -323 + 323 = 0 0 + -1n + n2 = 0 + 323 -1n + n2 = 0 + 323 Combine like terms: 0 + 323 = 323 -1n + n2 = 323 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 = 323 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 323 + 0.25 Combine like terms: 323 + 0.25 = 323.25 0.25 + -1n + n2 = 323.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 323.25 Calculate the square root of the right side: 17.979154596 Break this problem into two subproblems by setting (n + -0.5) equal to 17.979154596 and -17.979154596.Subproblem 1
n + -0.5 = 17.979154596 Simplifying n + -0.5 = 17.979154596 Reorder the terms: -0.5 + n = 17.979154596 Solving -0.5 + n = 17.979154596 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 = 17.979154596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 17.979154596 + 0.5 n = 17.979154596 + 0.5 Combine like terms: 17.979154596 + 0.5 = 18.479154596 n = 18.479154596 Simplifying n = 18.479154596Subproblem 2
n + -0.5 = -17.979154596 Simplifying n + -0.5 = -17.979154596 Reorder the terms: -0.5 + n = -17.979154596 Solving -0.5 + n = -17.979154596 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 = -17.979154596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -17.979154596 + 0.5 n = -17.979154596 + 0.5 Combine like terms: -17.979154596 + 0.5 = -17.479154596 n = -17.479154596 Simplifying n = -17.479154596Solution
The solution to the problem is based on the solutions from the subproblems. n = {18.479154596, -17.479154596}
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