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Simplifying n2 + n = 739 Reorder the terms: n + n2 = 739 Solving n + n2 = 739 Solving for variable 'n'. Reorder the terms: -739 + n + n2 = 739 + -739 Combine like terms: 739 + -739 = 0 -739 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '739' to each side of the equation. -739 + n + 739 + n2 = 0 + 739 Reorder the terms: -739 + 739 + n + n2 = 0 + 739 Combine like terms: -739 + 739 = 0 0 + n + n2 = 0 + 739 n + n2 = 0 + 739 Combine like terms: 0 + 739 = 739 n + n2 = 739 The n term is n. 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. n + 0.25 + n2 = 739 + 0.25 Reorder the terms: 0.25 + n + n2 = 739 + 0.25 Combine like terms: 739 + 0.25 = 739.25 0.25 + n + n2 = 739.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 739.25 Calculate the square root of the right side: 27.189152249 Break this problem into two subproblems by setting (n + 0.5) equal to 27.189152249 and -27.189152249.Subproblem 1
n + 0.5 = 27.189152249 Simplifying n + 0.5 = 27.189152249 Reorder the terms: 0.5 + n = 27.189152249 Solving 0.5 + n = 27.189152249 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 = 27.189152249 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 27.189152249 + -0.5 n = 27.189152249 + -0.5 Combine like terms: 27.189152249 + -0.5 = 26.689152249 n = 26.689152249 Simplifying n = 26.689152249Subproblem 2
n + 0.5 = -27.189152249 Simplifying n + 0.5 = -27.189152249 Reorder the terms: 0.5 + n = -27.189152249 Solving 0.5 + n = -27.189152249 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 = -27.189152249 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -27.189152249 + -0.5 n = -27.189152249 + -0.5 Combine like terms: -27.189152249 + -0.5 = -27.689152249 n = -27.689152249 Simplifying n = -27.689152249Solution
The solution to the problem is based on the solutions from the subproblems. n = {26.689152249, -27.689152249}
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