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Simplifying n2 + 2n = 0.65 Reorder the terms: 2n + n2 = 0.65 Solving 2n + n2 = 0.65 Solving for variable 'n'. Reorder the terms: -0.65 + 2n + n2 = 0.65 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 -0.65 + 2n + n2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.65' to each side of the equation. -0.65 + 2n + 0.65 + n2 = 0.00 + 0.65 Reorder the terms: -0.65 + 0.65 + 2n + n2 = 0.00 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + 2n + n2 = 0.00 + 0.65 2n + n2 = 0.00 + 0.65 Combine like terms: 0.00 + 0.65 = 0.65 2n + n2 = 0.65 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 = 0.65 + 1 Reorder the terms: 1 + 2n + n2 = 0.65 + 1 Combine like terms: 0.65 + 1 = 1.65 1 + 2n + n2 = 1.65 Factor a perfect square on the left side: (n + 1)(n + 1) = 1.65 Calculate the square root of the right side: 1.284523258 Break this problem into two subproblems by setting (n + 1) equal to 1.284523258 and -1.284523258.Subproblem 1
n + 1 = 1.284523258 Simplifying n + 1 = 1.284523258 Reorder the terms: 1 + n = 1.284523258 Solving 1 + n = 1.284523258 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 = 1.284523258 + -1 Combine like terms: 1 + -1 = 0 0 + n = 1.284523258 + -1 n = 1.284523258 + -1 Combine like terms: 1.284523258 + -1 = 0.284523258 n = 0.284523258 Simplifying n = 0.284523258Subproblem 2
n + 1 = -1.284523258 Simplifying n + 1 = -1.284523258 Reorder the terms: 1 + n = -1.284523258 Solving 1 + n = -1.284523258 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 = -1.284523258 + -1 Combine like terms: 1 + -1 = 0 0 + n = -1.284523258 + -1 n = -1.284523258 + -1 Combine like terms: -1.284523258 + -1 = -2.284523258 n = -2.284523258 Simplifying n = -2.284523258Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.284523258, -2.284523258}
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