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Simplifying x2 + -2x + -244 = 0 Reorder the terms: -244 + -2x + x2 = 0 Solving -244 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '244' to each side of the equation. -244 + -2x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + -2x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + -2x + x2 = 0 + 244 -2x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 -2x + x2 = 244 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 = 244 + 1 Reorder the terms: 1 + -2x + x2 = 244 + 1 Combine like terms: 244 + 1 = 245 1 + -2x + x2 = 245 Factor a perfect square on the left side: (x + -1)(x + -1) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (x + -1) equal to 15.652475842 and -15.652475842.Subproblem 1
x + -1 = 15.652475842 Simplifying x + -1 = 15.652475842 Reorder the terms: -1 + x = 15.652475842 Solving -1 + x = 15.652475842 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 = 15.652475842 + 1 Combine like terms: -1 + 1 = 0 0 + x = 15.652475842 + 1 x = 15.652475842 + 1 Combine like terms: 15.652475842 + 1 = 16.652475842 x = 16.652475842 Simplifying x = 16.652475842Subproblem 2
x + -1 = -15.652475842 Simplifying x + -1 = -15.652475842 Reorder the terms: -1 + x = -15.652475842 Solving -1 + x = -15.652475842 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 = -15.652475842 + 1 Combine like terms: -1 + 1 = 0 0 + x = -15.652475842 + 1 x = -15.652475842 + 1 Combine like terms: -15.652475842 + 1 = -14.652475842 x = -14.652475842 Simplifying x = -14.652475842Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.652475842, -14.652475842}
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