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Simplifying x2 + -13x + -23 = 0 Reorder the terms: -23 + -13x + x2 = 0 Solving -23 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -13x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -13x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -13x + x2 = 0 + 23 -13x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -13x + x2 = 23 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 = 23 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 23 + 42.25 Combine like terms: 23 + 42.25 = 65.25 42.25 + -13x + x2 = 65.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + -6.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + -6.5 = 8.077747211 Simplifying x + -6.5 = 8.077747211 Reorder the terms: -6.5 + x = 8.077747211 Solving -6.5 + x = 8.077747211 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 = 8.077747211 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.077747211 + 6.5 x = 8.077747211 + 6.5 Combine like terms: 8.077747211 + 6.5 = 14.577747211 x = 14.577747211 Simplifying x = 14.577747211Subproblem 2
x + -6.5 = -8.077747211 Simplifying x + -6.5 = -8.077747211 Reorder the terms: -6.5 + x = -8.077747211 Solving -6.5 + x = -8.077747211 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 = -8.077747211 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.077747211 + 6.5 x = -8.077747211 + 6.5 Combine like terms: -8.077747211 + 6.5 = -1.577747211 x = -1.577747211 Simplifying x = -1.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.577747211, -1.577747211}
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