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Simplifying 0 = -2x + x2 + -122 Reorder the terms: 0 = -122 + -2x + x2 Solving 0 = -122 + -2x + x2 Solving for variable 'x'. Combine like terms: 0 + 122 = 122 122 + 2x + -1x2 = -122 + -2x + x2 + 122 + 2x + -1x2 Reorder the terms: 122 + 2x + -1x2 = -122 + 122 + -2x + 2x + x2 + -1x2 Combine like terms: -122 + 122 = 0 122 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 122 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 122 + 2x + -1x2 = 0 + x2 + -1x2 122 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 122 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -122 + -2x + x2 = 0 Move the constant term to the right: Add '122' to each side of the equation. -122 + -2x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + -2x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + -2x + x2 = 0 + 122 -2x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 -2x + x2 = 122 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 122 + 1 Reorder the terms: 1 + -2x + x2 = 122 + 1 Combine like terms: 122 + 1 = 123 1 + -2x + x2 = 123 Factor a perfect square on the left side: (x + -1)(x + -1) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + -1) equal to 11.090536506 and -11.090536506.Subproblem 1
x + -1 = 11.090536506 Simplifying x + -1 = 11.090536506 Reorder the terms: -1 + x = 11.090536506 Solving -1 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 11.090536506 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.090536506 + 1 x = 11.090536506 + 1 Combine like terms: 11.090536506 + 1 = 12.090536506 x = 12.090536506 Simplifying x = 12.090536506Subproblem 2
x + -1 = -11.090536506 Simplifying x + -1 = -11.090536506 Reorder the terms: -1 + x = -11.090536506 Solving -1 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -11.090536506 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.090536506 + 1 x = -11.090536506 + 1 Combine like terms: -11.090536506 + 1 = -10.090536506 x = -10.090536506 Simplifying x = -10.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.090536506, -10.090536506}
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