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Simplifying 7n2 + 7n = 2 Reorder the terms: 7n + 7n2 = 2 Solving 7n + 7n2 = 2 Solving for variable 'n'. Reorder the terms: -2 + 7n + 7n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 7n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + n + n2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + n + 0.2857142857 + n2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + n + n2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + n + n2 = 0 + 0.2857142857 n + n2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 n + n2 = 0.2857142857 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + n2 = 0.2857142857 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = 0.2857142857 + 0.25 Combine like terms: 0.2857142857 + 0.25 = 0.5357142857 1.25 + n2 = 0.5357142857 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 0.5357142857 Calculate the square root of the right side: 0.731925055 Break this problem into two subproblems by setting (n + 0.5) equal to 0.731925055 and -0.731925055.Subproblem 1
n + 0.5 = 0.731925055 Simplifying n + 0.5 = 0.731925055 Reorder the terms: 0.5 + n = 0.731925055 Solving 0.5 + n = 0.731925055 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 0.731925055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 0.731925055 + -0.5 n = 0.731925055 + -0.5 Combine like terms: 0.731925055 + -0.5 = 0.231925055 n = 0.231925055 Simplifying n = 0.231925055Subproblem 2
n + 0.5 = -0.731925055 Simplifying n + 0.5 = -0.731925055 Reorder the terms: 0.5 + n = -0.731925055 Solving 0.5 + n = -0.731925055 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -0.731925055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -0.731925055 + -0.5 n = -0.731925055 + -0.5 Combine like terms: -0.731925055 + -0.5 = -1.231925055 n = -1.231925055 Simplifying n = -1.231925055Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.231925055, -1.231925055}
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