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Simplifying n2 + -2n = 6 Reorder the terms: -2n + n2 = 6 Solving -2n + n2 = 6 Solving for variable 'n'. Reorder the terms: -6 + -2n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -2n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2n + n2 = 0 + 6 -2n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2n + n2 = 6 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 6 + 1 Reorder the terms: 1 + -2n + n2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2n + n2 = 7 Factor a perfect square on the left side: (n + -1)(n + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (n + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
n + -1 = 2.645751311 Simplifying n + -1 = 2.645751311 Reorder the terms: -1 + n = 2.645751311 Solving -1 + n = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + n = 2.645751311 + 1 n = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 n = 3.645751311 Simplifying n = 3.645751311Subproblem 2
n + -1 = -2.645751311 Simplifying n + -1 = -2.645751311 Reorder the terms: -1 + n = -2.645751311 Solving -1 + n = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + n = -2.645751311 + 1 n = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 n = -1.645751311 Simplifying n = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.645751311, -1.645751311}
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