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Simplifying x2 + -13x + -82 = 0 Reorder the terms: -82 + -13x + x2 = 0 Solving -82 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -13x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + -13x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -13x + x2 = 0 + 82 -13x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 -13x + x2 = 82 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 = 82 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 82 + 42.25 Combine like terms: 82 + 42.25 = 124.25 42.25 + -13x + x2 = 124.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + -6.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + -6.5 = 11.146748405 Simplifying x + -6.5 = 11.146748405 Reorder the terms: -6.5 + x = 11.146748405 Solving -6.5 + x = 11.146748405 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 = 11.146748405 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 11.146748405 + 6.5 x = 11.146748405 + 6.5 Combine like terms: 11.146748405 + 6.5 = 17.646748405 x = 17.646748405 Simplifying x = 17.646748405Subproblem 2
x + -6.5 = -11.146748405 Simplifying x + -6.5 = -11.146748405 Reorder the terms: -6.5 + x = -11.146748405 Solving -6.5 + x = -11.146748405 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 = -11.146748405 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -11.146748405 + 6.5 x = -11.146748405 + 6.5 Combine like terms: -11.146748405 + 6.5 = -4.646748405 x = -4.646748405 Simplifying x = -4.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.646748405, -4.646748405}
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