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Simplifying x2 + 13x + 31 = 0 Reorder the terms: 31 + 13x + x2 = 0 Solving 31 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 13x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 13x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 13x + x2 = 0 + -31 13x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 13x + x2 = -31 The x term is 13x. 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. 13x + 42.25 + x2 = -31 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -31 + 42.25 Combine like terms: -31 + 42.25 = 11.25 42.25 + 13x + x2 = 11.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 6.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 6.5 = 3.354101966 Simplifying x + 6.5 = 3.354101966 Reorder the terms: 6.5 + x = 3.354101966 Solving 6.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 3.354101966 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 3.354101966 + -6.5 x = 3.354101966 + -6.5 Combine like terms: 3.354101966 + -6.5 = -3.145898034 x = -3.145898034 Simplifying x = -3.145898034Subproblem 2
x + 6.5 = -3.354101966 Simplifying x + 6.5 = -3.354101966 Reorder the terms: 6.5 + x = -3.354101966 Solving 6.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -3.354101966 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -3.354101966 + -6.5 x = -3.354101966 + -6.5 Combine like terms: -3.354101966 + -6.5 = -9.854101966 x = -9.854101966 Simplifying x = -9.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.145898034, -9.854101966}
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