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Simplifying n2 + 13n + 6 = 0 Reorder the terms: 6 + 13n + n2 = 0 Solving 6 + 13n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 13n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 13n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 13n + n2 = 0 + -6 13n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 13n + n2 = -6 The n term is 13n. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13n + 42.25 + n2 = -6 + 42.25 Reorder the terms: 42.25 + 13n + n2 = -6 + 42.25 Combine like terms: -6 + 42.25 = 36.25 42.25 + 13n + n2 = 36.25 Factor a perfect square on the left side: (n + 6.5)(n + 6.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (n + 6.5) equal to 6.020797289 and -6.020797289.Subproblem 1
n + 6.5 = 6.020797289 Simplifying n + 6.5 = 6.020797289 Reorder the terms: 6.5 + n = 6.020797289 Solving 6.5 + n = 6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = 6.020797289 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = 6.020797289 + -6.5 n = 6.020797289 + -6.5 Combine like terms: 6.020797289 + -6.5 = -0.479202711 n = -0.479202711 Simplifying n = -0.479202711Subproblem 2
n + 6.5 = -6.020797289 Simplifying n + 6.5 = -6.020797289 Reorder the terms: 6.5 + n = -6.020797289 Solving 6.5 + n = -6.020797289 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = -6.020797289 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = -6.020797289 + -6.5 n = -6.020797289 + -6.5 Combine like terms: -6.020797289 + -6.5 = -12.520797289 n = -12.520797289 Simplifying n = -12.520797289Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.479202711, -12.520797289}
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