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Simplifying n2 + -8n + -34 = 0 Reorder the terms: -34 + -8n + n2 = 0 Solving -34 + -8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -8n + 34 + n2 = 0 + 34 Reorder the terms: -34 + 34 + -8n + n2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -8n + n2 = 0 + 34 -8n + n2 = 0 + 34 Combine like terms: 0 + 34 = 34 -8n + n2 = 34 The n term is -8n. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8n + 16 + n2 = 34 + 16 Reorder the terms: 16 + -8n + n2 = 34 + 16 Combine like terms: 34 + 16 = 50 16 + -8n + n2 = 50 Factor a perfect square on the left side: (n + -4)(n + -4) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (n + -4) equal to 7.071067812 and -7.071067812.Subproblem 1
n + -4 = 7.071067812 Simplifying n + -4 = 7.071067812 Reorder the terms: -4 + n = 7.071067812 Solving -4 + n = 7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = 7.071067812 + 4 Combine like terms: -4 + 4 = 0 0 + n = 7.071067812 + 4 n = 7.071067812 + 4 Combine like terms: 7.071067812 + 4 = 11.071067812 n = 11.071067812 Simplifying n = 11.071067812Subproblem 2
n + -4 = -7.071067812 Simplifying n + -4 = -7.071067812 Reorder the terms: -4 + n = -7.071067812 Solving -4 + n = -7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + n = -7.071067812 + 4 Combine like terms: -4 + 4 = 0 0 + n = -7.071067812 + 4 n = -7.071067812 + 4 Combine like terms: -7.071067812 + 4 = -3.071067812 n = -3.071067812 Simplifying n = -3.071067812Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.071067812, -3.071067812}
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