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Simplifying x2 + -22x + 121 = 131 Reorder the terms: 121 + -22x + x2 = 131 Solving 121 + -22x + x2 = 131 Solving for variable 'x'. Reorder the terms: 121 + -131 + -22x + x2 = 131 + -131 Combine like terms: 121 + -131 = -10 -10 + -22x + x2 = 131 + -131 Combine like terms: 131 + -131 = 0 -10 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -22x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -22x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -22x + x2 = 0 + 10 -22x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -22x + x2 = 10 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 = 10 + 121 Reorder the terms: 121 + -22x + x2 = 10 + 121 Combine like terms: 10 + 121 = 131 121 + -22x + x2 = 131 Factor a perfect square on the left side: (x + -11)(x + -11) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + -11) equal to 11.445523142 and -11.445523142.Subproblem 1
x + -11 = 11.445523142 Simplifying x + -11 = 11.445523142 Reorder the terms: -11 + x = 11.445523142 Solving -11 + x = 11.445523142 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 = 11.445523142 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.445523142 + 11 x = 11.445523142 + 11 Combine like terms: 11.445523142 + 11 = 22.445523142 x = 22.445523142 Simplifying x = 22.445523142Subproblem 2
x + -11 = -11.445523142 Simplifying x + -11 = -11.445523142 Reorder the terms: -11 + x = -11.445523142 Solving -11 + x = -11.445523142 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 = -11.445523142 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.445523142 + 11 x = -11.445523142 + 11 Combine like terms: -11.445523142 + 11 = -0.445523142 x = -0.445523142 Simplifying x = -0.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.445523142, -0.445523142}
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