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Simplifying n2 + -11n + 7 = 0 Reorder the terms: 7 + -11n + n2 = 0 Solving 7 + -11n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -11n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + -11n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -11n + n2 = 0 + -7 -11n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -11n + n2 = -7 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = -7 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -7 + 30.25 Combine like terms: -7 + 30.25 = 23.25 30.25 + -11n + n2 = 23.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (n + -5.5) equal to 4.82182538 and -4.82182538.Subproblem 1
n + -5.5 = 4.82182538 Simplifying n + -5.5 = 4.82182538 Reorder the terms: -5.5 + n = 4.82182538 Solving -5.5 + n = 4.82182538 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 4.82182538 + 5.5 n = 4.82182538 + 5.5 Combine like terms: 4.82182538 + 5.5 = 10.32182538 n = 10.32182538 Simplifying n = 10.32182538Subproblem 2
n + -5.5 = -4.82182538 Simplifying n + -5.5 = -4.82182538 Reorder the terms: -5.5 + n = -4.82182538 Solving -5.5 + n = -4.82182538 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -4.82182538 + 5.5 n = -4.82182538 + 5.5 Combine like terms: -4.82182538 + 5.5 = 0.67817462 n = 0.67817462 Simplifying n = 0.67817462Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.32182538, 0.67817462}
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