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Simplifying x2 + x + -196 = 244 Reorder the terms: -196 + x + x2 = 244 Solving -196 + x + x2 = 244 Solving for variable 'x'. Reorder the terms: -196 + -244 + x + x2 = 244 + -244 Combine like terms: -196 + -244 = -440 -440 + x + x2 = 244 + -244 Combine like terms: 244 + -244 = 0 -440 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '440' to each side of the equation. -440 + x + 440 + x2 = 0 + 440 Reorder the terms: -440 + 440 + x + x2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + x + x2 = 0 + 440 x + x2 = 0 + 440 Combine like terms: 0 + 440 = 440 x + x2 = 440 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 440 + 0.25 Reorder the terms: 0.25 + x + x2 = 440 + 0.25 Combine like terms: 440 + 0.25 = 440.25 0.25 + x + x2 = 440.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 440.25 Calculate the square root of the right side: 20.982135258 Break this problem into two subproblems by setting (x + 0.5) equal to 20.982135258 and -20.982135258.Subproblem 1
x + 0.5 = 20.982135258 Simplifying x + 0.5 = 20.982135258 Reorder the terms: 0.5 + x = 20.982135258 Solving 0.5 + x = 20.982135258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 20.982135258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 20.982135258 + -0.5 x = 20.982135258 + -0.5 Combine like terms: 20.982135258 + -0.5 = 20.482135258 x = 20.482135258 Simplifying x = 20.482135258Subproblem 2
x + 0.5 = -20.982135258 Simplifying x + 0.5 = -20.982135258 Reorder the terms: 0.5 + x = -20.982135258 Solving 0.5 + x = -20.982135258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -20.982135258 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -20.982135258 + -0.5 x = -20.982135258 + -0.5 Combine like terms: -20.982135258 + -0.5 = -21.482135258 x = -21.482135258 Simplifying x = -21.482135258Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.482135258, -21.482135258}
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