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Simplifying x2 + -22x + 11 = 0 Reorder the terms: 11 + -22x + x2 = 0 Solving 11 + -22x + 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 + -22x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -22x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -22x + x2 = 0 + -11 -22x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -22x + x2 = -11 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 = -11 + 121 Reorder the terms: 121 + -22x + x2 = -11 + 121 Combine like terms: -11 + 121 = 110 121 + -22x + x2 = 110 Factor a perfect square on the left side: (x + -11)(x + -11) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + -11) equal to 10.488088482 and -10.488088482.Subproblem 1
x + -11 = 10.488088482 Simplifying x + -11 = 10.488088482 Reorder the terms: -11 + x = 10.488088482 Solving -11 + x = 10.488088482 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 = 10.488088482 + 11 Combine like terms: -11 + 11 = 0 0 + x = 10.488088482 + 11 x = 10.488088482 + 11 Combine like terms: 10.488088482 + 11 = 21.488088482 x = 21.488088482 Simplifying x = 21.488088482Subproblem 2
x + -11 = -10.488088482 Simplifying x + -11 = -10.488088482 Reorder the terms: -11 + x = -10.488088482 Solving -11 + x = -10.488088482 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 = -10.488088482 + 11 Combine like terms: -11 + 11 = 0 0 + x = -10.488088482 + 11 x = -10.488088482 + 11 Combine like terms: -10.488088482 + 11 = 0.511911518 x = 0.511911518 Simplifying x = 0.511911518Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.488088482, 0.511911518}
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