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Simplifying 2n2 = n + 2 Reorder the terms: 2n2 = 2 + n Solving 2n2 = 2 + n Solving for variable 'n'. Reorder the terms: -2 + -1n + 2n2 = 2 + n + -2 + -1n Reorder the terms: -2 + -1n + 2n2 = 2 + -2 + n + -1n Combine like terms: 2 + -2 = 0 -2 + -1n + 2n2 = 0 + n + -1n -2 + -1n + 2n2 = n + -1n Combine like terms: n + -1n = 0 -2 + -1n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -0.5n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5n + n2 = 0 + 1 -0.5n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5n + n2 = 1 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5n + n2 = 1.0625 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (n + -0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
n + -0.25 = 1.030776406 Simplifying n + -0.25 = 1.030776406 Reorder the terms: -0.25 + n = 1.030776406 Solving -0.25 + n = 1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = 1.030776406 + 0.25 n = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 n = 1.280776406 Simplifying n = 1.280776406Subproblem 2
n + -0.25 = -1.030776406 Simplifying n + -0.25 = -1.030776406 Reorder the terms: -0.25 + n = -1.030776406 Solving -0.25 + n = -1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = -1.030776406 + 0.25 n = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 n = -0.780776406 Simplifying n = -0.780776406Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.280776406, -0.780776406}
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