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Simplifying n2 + 5n + -139 = 0 Reorder the terms: -139 + 5n + n2 = 0 Solving -139 + 5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '139' to each side of the equation. -139 + 5n + 139 + n2 = 0 + 139 Reorder the terms: -139 + 139 + 5n + n2 = 0 + 139 Combine like terms: -139 + 139 = 0 0 + 5n + n2 = 0 + 139 5n + n2 = 0 + 139 Combine like terms: 0 + 139 = 139 5n + n2 = 139 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 139 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 139 + 6.25 Combine like terms: 139 + 6.25 = 145.25 6.25 + 5n + n2 = 145.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (n + 2.5) equal to 12.051970793 and -12.051970793.Subproblem 1
n + 2.5 = 12.051970793 Simplifying n + 2.5 = 12.051970793 Reorder the terms: 2.5 + n = 12.051970793 Solving 2.5 + n = 12.051970793 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 12.051970793 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 12.051970793 + -2.5 n = 12.051970793 + -2.5 Combine like terms: 12.051970793 + -2.5 = 9.551970793 n = 9.551970793 Simplifying n = 9.551970793Subproblem 2
n + 2.5 = -12.051970793 Simplifying n + 2.5 = -12.051970793 Reorder the terms: 2.5 + n = -12.051970793 Solving 2.5 + n = -12.051970793 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -12.051970793 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -12.051970793 + -2.5 n = -12.051970793 + -2.5 Combine like terms: -12.051970793 + -2.5 = -14.551970793 n = -14.551970793 Simplifying n = -14.551970793Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.551970793, -14.551970793}
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