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Simplifying n2 + -16n + 14 = 0 Reorder the terms: 14 + -16n + n2 = 0 Solving 14 + -16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -16n + -14 + n2 = 0 + -14 Reorder the terms: 14 + -14 + -16n + n2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -16n + n2 = 0 + -14 -16n + n2 = 0 + -14 Combine like terms: 0 + -14 = -14 -16n + n2 = -14 The n term is -16n. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16n + 64 + n2 = -14 + 64 Reorder the terms: 64 + -16n + n2 = -14 + 64 Combine like terms: -14 + 64 = 50 64 + -16n + n2 = 50 Factor a perfect square on the left side: (n + -8)(n + -8) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (n + -8) equal to 7.071067812 and -7.071067812.Subproblem 1
n + -8 = 7.071067812 Simplifying n + -8 = 7.071067812 Reorder the terms: -8 + n = 7.071067812 Solving -8 + n = 7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = 7.071067812 + 8 Combine like terms: -8 + 8 = 0 0 + n = 7.071067812 + 8 n = 7.071067812 + 8 Combine like terms: 7.071067812 + 8 = 15.071067812 n = 15.071067812 Simplifying n = 15.071067812Subproblem 2
n + -8 = -7.071067812 Simplifying n + -8 = -7.071067812 Reorder the terms: -8 + n = -7.071067812 Solving -8 + n = -7.071067812 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = -7.071067812 + 8 Combine like terms: -8 + 8 = 0 0 + n = -7.071067812 + 8 n = -7.071067812 + 8 Combine like terms: -7.071067812 + 8 = 0.928932188 n = 0.928932188 Simplifying n = 0.928932188Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.071067812, 0.928932188}
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