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Simplifying n2 + -1n + -29 = 0 Reorder the terms: -29 + -1n + n2 = 0 Solving -29 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -1n + 29 + n2 = 0 + 29 Reorder the terms: -29 + 29 + -1n + n2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1n + n2 = 0 + 29 -1n + n2 = 0 + 29 Combine like terms: 0 + 29 = 29 -1n + n2 = 29 The n term is -1n. 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. -1n + 0.25 + n2 = 29 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 0.25 + -1n + n2 = 29.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (n + -0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
n + -0.5 = 5.408326913 Simplifying n + -0.5 = 5.408326913 Reorder the terms: -0.5 + n = 5.408326913 Solving -0.5 + n = 5.408326913 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 = 5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 5.408326913 + 0.5 n = 5.408326913 + 0.5 Combine like terms: 5.408326913 + 0.5 = 5.908326913 n = 5.908326913 Simplifying n = 5.908326913Subproblem 2
n + -0.5 = -5.408326913 Simplifying n + -0.5 = -5.408326913 Reorder the terms: -0.5 + n = -5.408326913 Solving -0.5 + n = -5.408326913 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 = -5.408326913 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -5.408326913 + 0.5 n = -5.408326913 + 0.5 Combine like terms: -5.408326913 + 0.5 = -4.908326913 n = -4.908326913 Simplifying n = -4.908326913Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.908326913, -4.908326913}
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