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Simplifying n2 + 7n + -11 = 0 Reorder the terms: -11 + 7n + n2 = 0 Solving -11 + 7n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 7n + 11 + n2 = 0 + 11 Reorder the terms: -11 + 11 + 7n + n2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 7n + n2 = 0 + 11 7n + n2 = 0 + 11 Combine like terms: 0 + 11 = 11 7n + n2 = 11 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 11 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 11 + 12.25 Combine like terms: 11 + 12.25 = 23.25 12.25 + 7n + n2 = 23.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (n + 3.5) equal to 4.82182538 and -4.82182538.Subproblem 1
n + 3.5 = 4.82182538 Simplifying n + 3.5 = 4.82182538 Reorder the terms: 3.5 + n = 4.82182538 Solving 3.5 + n = 4.82182538 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 4.82182538 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 4.82182538 + -3.5 n = 4.82182538 + -3.5 Combine like terms: 4.82182538 + -3.5 = 1.32182538 n = 1.32182538 Simplifying n = 1.32182538Subproblem 2
n + 3.5 = -4.82182538 Simplifying n + 3.5 = -4.82182538 Reorder the terms: 3.5 + n = -4.82182538 Solving 3.5 + n = -4.82182538 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -4.82182538 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -4.82182538 + -3.5 n = -4.82182538 + -3.5 Combine like terms: -4.82182538 + -3.5 = -8.32182538 n = -8.32182538 Simplifying n = -8.32182538Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.32182538, -8.32182538}
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