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Simplifying x2 + x = 500000000000000000 Reorder the terms: x + x2 = 500000000000000000 Solving x + x2 = 500000000000000000 Solving for variable 'x'. Reorder the terms: -500000000000000000 + x + x2 = 500000000000000000 + -500000000000000000 Combine like terms: 500000000000000000 + -500000000000000000 = 0 -500000000000000000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500000000000000000' to each side of the equation. -500000000000000000 + x + 500000000000000000 + x2 = 0 + 500000000000000000 Reorder the terms: -500000000000000000 + 500000000000000000 + x + x2 = 0 + 500000000000000000 Combine like terms: -500000000000000000 + 500000000000000000 = 0 0 + x + x2 = 0 + 500000000000000000 x + x2 = 0 + 500000000000000000 Combine like terms: 0 + 500000000000000000 = 500000000000000000 x + x2 = 500000000000000000 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 = 500000000000000000 + 0.25 Reorder the terms: 0.25 + x + x2 = 500000000000000000 + 0.25 Combine like terms: 500000000000000000 + 0.25 = 500000000000000000.25 0.25 + x + x2 = 500000000000000000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 500000000000000000.25 Calculate the square root of the right side: 707106781.186547525 Break this problem into two subproblems by setting (x + 0.5) equal to 707106781.186547525 and -707106781.186547525.Subproblem 1
x + 0.5 = 707106781.186547525 Simplifying x + 0.5 = 707106781.186547525 Reorder the terms: 0.5 + x = 707106781.186547525 Solving 0.5 + x = 707106781.186547525 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 = 707106781.186547525 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 707106781.186547525 + -0.5 x = 707106781.186547525 + -0.5 Combine like terms: 707106781.186547525 + -0.5 = 707106780.686547525 x = 707106780.686547525 Simplifying x = 707106780.686547525Subproblem 2
x + 0.5 = -707106781.186547525 Simplifying x + 0.5 = -707106781.186547525 Reorder the terms: 0.5 + x = -707106781.186547525 Solving 0.5 + x = -707106781.186547525 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 = -707106781.186547525 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -707106781.186547525 + -0.5 x = -707106781.186547525 + -0.5 Combine like terms: -707106781.186547525 + -0.5 = -707106781.686547525 x = -707106781.686547525 Simplifying x = -707106781.686547525Solution
The solution to the problem is based on the solutions from the subproblems. x = {707106780.686547525, -707106781.686547525}
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