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Simplifying x2 + -55x + 11 = 0 Reorder the terms: 11 + -55x + x2 = 0 Solving 11 + -55x + 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 + -55x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -55x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -55x + x2 = 0 + -11 -55x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -55x + x2 = -11 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -11 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -11 + 756.25 Combine like terms: -11 + 756.25 = 745.25 756.25 + -55x + x2 = 745.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 745.25 Calculate the square root of the right side: 27.299267389 Break this problem into two subproblems by setting (x + -27.5) equal to 27.299267389 and -27.299267389.Subproblem 1
x + -27.5 = 27.299267389 Simplifying x + -27.5 = 27.299267389 Reorder the terms: -27.5 + x = 27.299267389 Solving -27.5 + x = 27.299267389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 27.299267389 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 27.299267389 + 27.5 x = 27.299267389 + 27.5 Combine like terms: 27.299267389 + 27.5 = 54.799267389 x = 54.799267389 Simplifying x = 54.799267389Subproblem 2
x + -27.5 = -27.299267389 Simplifying x + -27.5 = -27.299267389 Reorder the terms: -27.5 + x = -27.299267389 Solving -27.5 + x = -27.299267389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -27.299267389 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -27.299267389 + 27.5 x = -27.299267389 + 27.5 Combine like terms: -27.299267389 + 27.5 = 0.200732611 x = 0.200732611 Simplifying x = 0.200732611Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.799267389, 0.200732611}
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