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Simplifying n(n + 2) = 56 Reorder the terms: n(2 + n) = 56 (2 * n + n * n) = 56 (2n + n2) = 56 Solving 2n + n2 = 56 Solving for variable 'n'. Reorder the terms: -56 + 2n + n2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 2n + 56 + n2 = 0 + 56 Reorder the terms: -56 + 56 + 2n + n2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 2n + n2 = 0 + 56 2n + n2 = 0 + 56 Combine like terms: 0 + 56 = 56 2n + n2 = 56 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 = 56 + 1 Reorder the terms: 1 + 2n + n2 = 56 + 1 Combine like terms: 56 + 1 = 57 1 + 2n + n2 = 57 Factor a perfect square on the left side: (n + 1)(n + 1) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (n + 1) equal to 7.549834435 and -7.549834435.Subproblem 1
n + 1 = 7.549834435 Simplifying n + 1 = 7.549834435 Reorder the terms: 1 + n = 7.549834435 Solving 1 + n = 7.549834435 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 = 7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + n = 7.549834435 + -1 n = 7.549834435 + -1 Combine like terms: 7.549834435 + -1 = 6.549834435 n = 6.549834435 Simplifying n = 6.549834435Subproblem 2
n + 1 = -7.549834435 Simplifying n + 1 = -7.549834435 Reorder the terms: 1 + n = -7.549834435 Solving 1 + n = -7.549834435 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 = -7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + n = -7.549834435 + -1 n = -7.549834435 + -1 Combine like terms: -7.549834435 + -1 = -8.549834435 n = -8.549834435 Simplifying n = -8.549834435Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.549834435, -8.549834435}
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