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Simplifying x2 + -22x + -271 = 0 Reorder the terms: -271 + -22x + x2 = 0 Solving -271 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '271' to each side of the equation. -271 + -22x + 271 + x2 = 0 + 271 Reorder the terms: -271 + 271 + -22x + x2 = 0 + 271 Combine like terms: -271 + 271 = 0 0 + -22x + x2 = 0 + 271 -22x + x2 = 0 + 271 Combine like terms: 0 + 271 = 271 -22x + x2 = 271 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 271 + 121 Reorder the terms: 121 + -22x + x2 = 271 + 121 Combine like terms: 271 + 121 = 392 121 + -22x + x2 = 392 Factor a perfect square on the left side: (x + -11)(x + -11) = 392 Calculate the square root of the right side: 19.798989873 Break this problem into two subproblems by setting (x + -11) equal to 19.798989873 and -19.798989873.Subproblem 1
x + -11 = 19.798989873 Simplifying x + -11 = 19.798989873 Reorder the terms: -11 + x = 19.798989873 Solving -11 + x = 19.798989873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 19.798989873 + 11 Combine like terms: -11 + 11 = 0 0 + x = 19.798989873 + 11 x = 19.798989873 + 11 Combine like terms: 19.798989873 + 11 = 30.798989873 x = 30.798989873 Simplifying x = 30.798989873Subproblem 2
x + -11 = -19.798989873 Simplifying x + -11 = -19.798989873 Reorder the terms: -11 + x = -19.798989873 Solving -11 + x = -19.798989873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -19.798989873 + 11 Combine like terms: -11 + 11 = 0 0 + x = -19.798989873 + 11 x = -19.798989873 + 11 Combine like terms: -19.798989873 + 11 = -8.798989873 x = -8.798989873 Simplifying x = -8.798989873Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.798989873, -8.798989873}
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