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Simplifying x2 + -13x + -11 = 0 Reorder the terms: -11 + -13x + x2 = 0 Solving -11 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -13x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -13x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -13x + x2 = 0 + 11 -13x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -13x + x2 = 11 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 = 11 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 11 + 42.25 Combine like terms: 11 + 42.25 = 53.25 42.25 + -13x + x2 = 53.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + -6.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + -6.5 = 7.29725976 Simplifying x + -6.5 = 7.29725976 Reorder the terms: -6.5 + x = 7.29725976 Solving -6.5 + x = 7.29725976 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 = 7.29725976 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.29725976 + 6.5 x = 7.29725976 + 6.5 Combine like terms: 7.29725976 + 6.5 = 13.79725976 x = 13.79725976 Simplifying x = 13.79725976Subproblem 2
x + -6.5 = -7.29725976 Simplifying x + -6.5 = -7.29725976 Reorder the terms: -6.5 + x = -7.29725976 Solving -6.5 + x = -7.29725976 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 = -7.29725976 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.29725976 + 6.5 x = -7.29725976 + 6.5 Combine like terms: -7.29725976 + 6.5 = -0.79725976 x = -0.79725976 Simplifying x = -0.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.79725976, -0.79725976}
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