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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 = 9.854101966 x = 9.854101966 Simplifying x = 9.854101966Subproblem 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 = 3.145898034 x = 3.145898034 Simplifying x = 3.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.854101966, 3.145898034}
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