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Simplifying x(x + 1) = 4294967294 Reorder the terms: x(1 + x) = 4294967294 (1 * x + x * x) = 4294967294 (1x + x2) = 4294967294 Solving 1x + x2 = 4294967294 Solving for variable 'x'. Reorder the terms: -4294967294 + 1x + x2 = 4294967294 + -4294967294 Combine like terms: 4294967294 + -4294967294 = 0 -4294967294 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4294967294' to each side of the equation. -4294967294 + 1x + 4294967294 + x2 = 0 + 4294967294 Reorder the terms: -4294967294 + 4294967294 + 1x + x2 = 0 + 4294967294 Combine like terms: -4294967294 + 4294967294 = 0 0 + 1x + x2 = 0 + 4294967294 1x + x2 = 0 + 4294967294 Combine like terms: 0 + 4294967294 = 4294967294 1x + x2 = 4294967294 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. x + 0.25 + x2 = 4294967294 + 0.25 Reorder the terms: 0.25 + x + x2 = 4294967294 + 0.25 Combine like terms: 4294967294 + 0.25 = 4294967294.25 0.25 + x + x2 = 4294967294.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4294967294.25 Calculate the square root of the right side: 65535.999986649 Break this problem into two subproblems by setting (x + 0.5) equal to 65535.999986649 and -65535.999986649.Subproblem 1
x + 0.5 = 65535.999986649 Simplifying x + 0.5 = 65535.999986649 Reorder the terms: 0.5 + x = 65535.999986649 Solving 0.5 + x = 65535.999986649 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 = 65535.999986649 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 65535.999986649 + -0.5 x = 65535.999986649 + -0.5 Combine like terms: 65535.999986649 + -0.5 = 65535.499986649 x = 65535.499986649 Simplifying x = 65535.499986649Subproblem 2
x + 0.5 = -65535.999986649 Simplifying x + 0.5 = -65535.999986649 Reorder the terms: 0.5 + x = -65535.999986649 Solving 0.5 + x = -65535.999986649 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 = -65535.999986649 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -65535.999986649 + -0.5 x = -65535.999986649 + -0.5 Combine like terms: -65535.999986649 + -0.5 = -65536.499986649 x = -65536.499986649 Simplifying x = -65536.499986649Solution
The solution to the problem is based on the solutions from the subproblems. x = {65535.499986649, -65536.499986649}
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