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Simplifying n2 + 2n + -74 = 0 Reorder the terms: -74 + 2n + n2 = 0 Solving -74 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 2n + 74 + n2 = 0 + 74 Reorder the terms: -74 + 74 + 2n + n2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 2n + n2 = 0 + 74 2n + n2 = 0 + 74 Combine like terms: 0 + 74 = 74 2n + n2 = 74 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 = 74 + 1 Reorder the terms: 1 + 2n + n2 = 74 + 1 Combine like terms: 74 + 1 = 75 1 + 2n + n2 = 75 Factor a perfect square on the left side: (n + 1)(n + 1) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (n + 1) equal to 8.660254038 and -8.660254038.Subproblem 1
n + 1 = 8.660254038 Simplifying n + 1 = 8.660254038 Reorder the terms: 1 + n = 8.660254038 Solving 1 + n = 8.660254038 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 = 8.660254038 + -1 Combine like terms: 1 + -1 = 0 0 + n = 8.660254038 + -1 n = 8.660254038 + -1 Combine like terms: 8.660254038 + -1 = 7.660254038 n = 7.660254038 Simplifying n = 7.660254038Subproblem 2
n + 1 = -8.660254038 Simplifying n + 1 = -8.660254038 Reorder the terms: 1 + n = -8.660254038 Solving 1 + n = -8.660254038 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 = -8.660254038 + -1 Combine like terms: 1 + -1 = 0 0 + n = -8.660254038 + -1 n = -8.660254038 + -1 Combine like terms: -8.660254038 + -1 = -9.660254038 n = -9.660254038 Simplifying n = -9.660254038Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.660254038, -9.660254038}
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