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Simplifying x2 = 11x + -1 Reorder the terms: x2 = -1 + 11x Solving x2 = -1 + 11x Solving for variable 'x'. Reorder the terms: 1 + -11x + x2 = -1 + 11x + 1 + -11x Reorder the terms: 1 + -11x + x2 = -1 + 1 + 11x + -11x Combine like terms: -1 + 1 = 0 1 + -11x + x2 = 0 + 11x + -11x 1 + -11x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 1 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -11x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11x + x2 = 0 + -1 -11x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11x + x2 = -1 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -1 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11x + x2 = 29.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -5.5 = 5.408326913 Simplifying x + -5.5 = 5.408326913 Reorder the terms: -5.5 + x = 5.408326913 Solving -5.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.408326913 + 5.5 x = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 x = 10.908326913 Simplifying x = 10.908326913Subproblem 2
x + -5.5 = -5.408326913 Simplifying x + -5.5 = -5.408326913 Reorder the terms: -5.5 + x = -5.408326913 Solving -5.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.408326913 + 5.5 x = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 x = 0.091673087 Simplifying x = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.908326913, 0.091673087}
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