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Simplifying x2 + x + -2441 = 0 Reorder the terms: -2441 + x + x2 = 0 Solving -2441 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2441' to each side of the equation. -2441 + x + 2441 + x2 = 0 + 2441 Reorder the terms: -2441 + 2441 + x + x2 = 0 + 2441 Combine like terms: -2441 + 2441 = 0 0 + x + x2 = 0 + 2441 x + x2 = 0 + 2441 Combine like terms: 0 + 2441 = 2441 x + x2 = 2441 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 = 2441 + 0.25 Reorder the terms: 0.25 + x + x2 = 2441 + 0.25 Combine like terms: 2441 + 0.25 = 2441.25 0.25 + x + x2 = 2441.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2441.25 Calculate the square root of the right side: 49.409007276 Break this problem into two subproblems by setting (x + 0.5) equal to 49.409007276 and -49.409007276.Subproblem 1
x + 0.5 = 49.409007276 Simplifying x + 0.5 = 49.409007276 Reorder the terms: 0.5 + x = 49.409007276 Solving 0.5 + x = 49.409007276 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 = 49.409007276 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 49.409007276 + -0.5 x = 49.409007276 + -0.5 Combine like terms: 49.409007276 + -0.5 = 48.909007276 x = 48.909007276 Simplifying x = 48.909007276Subproblem 2
x + 0.5 = -49.409007276 Simplifying x + 0.5 = -49.409007276 Reorder the terms: 0.5 + x = -49.409007276 Solving 0.5 + x = -49.409007276 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 = -49.409007276 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -49.409007276 + -0.5 x = -49.409007276 + -0.5 Combine like terms: -49.409007276 + -0.5 = -49.909007276 x = -49.909007276 Simplifying x = -49.909007276Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.909007276, -49.909007276}
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