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Simplifying x2 + -100000000x + 1 = 0 Reorder the terms: 1 + -100000000x + x2 = 0 Solving 1 + -100000000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -100000000x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -100000000x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -100000000x + x2 = 0 + -1 -100000000x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -100000000x + x2 = -1 The x term is -100000000x. Take half its coefficient (-50000000). Square it (2500000000000000) and add it to both sides. Add '2500000000000000' to each side of the equation. -100000000x + 2500000000000000 + x2 = -1 + 2500000000000000 Reorder the terms: 2500000000000000 + -100000000x + x2 = -1 + 2500000000000000 Combine like terms: -1 + 2500000000000000 = 2499999999999999 2500000000000000 + -100000000x + x2 = 2499999999999999 Factor a perfect square on the left side: (x + -50000000)(x + -50000000) = 2499999999999999 Calculate the square root of the right side: 49999999.99999999 Break this problem into two subproblems by setting (x + -50000000) equal to 49999999.99999999 and -49999999.99999999.Subproblem 1
x + -50000000 = 49999999.99999999 Simplifying x + -50000000 = 49999999.99999999 Reorder the terms: -50000000 + x = 49999999.99999999 Solving -50000000 + x = 49999999.99999999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000000' to each side of the equation. -50000000 + 50000000 + x = 49999999.99999999 + 50000000 Combine like terms: -50000000 + 50000000 = 0 0 + x = 49999999.99999999 + 50000000 x = 49999999.99999999 + 50000000 Combine like terms: 49999999.99999999 + 50000000 = 99999999.99999999 x = 99999999.99999999 Simplifying x = 99999999.99999999Subproblem 2
x + -50000000 = -49999999.99999999 Simplifying x + -50000000 = -49999999.99999999 Reorder the terms: -50000000 + x = -49999999.99999999 Solving -50000000 + x = -49999999.99999999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000000' to each side of the equation. -50000000 + 50000000 + x = -49999999.99999999 + 50000000 Combine like terms: -50000000 + 50000000 = 0 0 + x = -49999999.99999999 + 50000000 x = -49999999.99999999 + 50000000 Combine like terms: -49999999.99999999 + 50000000 = 0.00000001 x = 0.00000001 Simplifying x = 0.00000001Solution
The solution to the problem is based on the solutions from the subproblems. x = {99999999.99999999, 0.00000001}
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