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Simplifying x2 + -1x + -2446 = 0 Reorder the terms: -2446 + -1x + x2 = 0 Solving -2446 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2446' to each side of the equation. -2446 + -1x + 2446 + x2 = 0 + 2446 Reorder the terms: -2446 + 2446 + -1x + x2 = 0 + 2446 Combine like terms: -2446 + 2446 = 0 0 + -1x + x2 = 0 + 2446 -1x + x2 = 0 + 2446 Combine like terms: 0 + 2446 = 2446 -1x + x2 = 2446 The x term is -1x. 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. -1x + 0.25 + x2 = 2446 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2446 + 0.25 Combine like terms: 2446 + 0.25 = 2446.25 0.25 + -1x + x2 = 2446.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2446.25 Calculate the square root of the right side: 49.459579456 Break this problem into two subproblems by setting (x + -0.5) equal to 49.459579456 and -49.459579456.Subproblem 1
x + -0.5 = 49.459579456 Simplifying x + -0.5 = 49.459579456 Reorder the terms: -0.5 + x = 49.459579456 Solving -0.5 + x = 49.459579456 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 = 49.459579456 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 49.459579456 + 0.5 x = 49.459579456 + 0.5 Combine like terms: 49.459579456 + 0.5 = 49.959579456 x = 49.959579456 Simplifying x = 49.959579456Subproblem 2
x + -0.5 = -49.459579456 Simplifying x + -0.5 = -49.459579456 Reorder the terms: -0.5 + x = -49.459579456 Solving -0.5 + x = -49.459579456 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 = -49.459579456 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -49.459579456 + 0.5 x = -49.459579456 + 0.5 Combine like terms: -49.459579456 + 0.5 = -48.959579456 x = -48.959579456 Simplifying x = -48.959579456Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.959579456, -48.959579456}
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