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Simplifying x4 + -127000x2 + -20570000000 = 0 Reorder the terms: -20570000000 + -127000x2 + x4 = 0 Solving -20570000000 + -127000x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20570000000' to each side of the equation. -20570000000 + -127000x2 + 20570000000 + x4 = 0 + 20570000000 Reorder the terms: -20570000000 + 20570000000 + -127000x2 + x4 = 0 + 20570000000 Combine like terms: -20570000000 + 20570000000 = 0 0 + -127000x2 + x4 = 0 + 20570000000 -127000x2 + x4 = 0 + 20570000000 Combine like terms: 0 + 20570000000 = 20570000000 -127000x2 + x4 = 20570000000 The x term is -127000x2. Take half its coefficient (-63500). Square it (4032250000) and add it to both sides. Add '4032250000' to each side of the equation. -127000x2 + 4032250000 + x4 = 20570000000 + 4032250000 Reorder the terms: 4032250000 + -127000x2 + x4 = 20570000000 + 4032250000 Combine like terms: 20570000000 + 4032250000 = 24602250000 4032250000 + -127000x2 + x4 = 24602250000 Factor a perfect square on the left side: (x2 + -63500)(x2 + -63500) = 24602250000 Calculate the square root of the right side: 156851.0439876 Break this problem into two subproblems by setting (x2 + -63500) equal to 156851.0439876 and -156851.0439876.Subproblem 1
x2 + -63500 = 156851.0439876 Simplifying x2 + -63500 = 156851.0439876 Reorder the terms: -63500 + x2 = 156851.0439876 Solving -63500 + x2 = 156851.0439876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63500' to each side of the equation. -63500 + 63500 + x2 = 156851.0439876 + 63500 Combine like terms: -63500 + 63500 = 0 0 + x2 = 156851.0439876 + 63500 x2 = 156851.0439876 + 63500 Combine like terms: 156851.0439876 + 63500 = 220351.0439876 x2 = 220351.0439876 Simplifying x2 = 220351.0439876 Take the square root of each side: x = {-469.41564097, 469.41564097}Subproblem 2
x2 + -63500 = -156851.0439876 Simplifying x2 + -63500 = -156851.0439876 Reorder the terms: -63500 + x2 = -156851.0439876 Solving -63500 + x2 = -156851.0439876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63500' to each side of the equation. -63500 + 63500 + x2 = -156851.0439876 + 63500 Combine like terms: -63500 + 63500 = 0 0 + x2 = -156851.0439876 + 63500 x2 = -156851.0439876 + 63500 Combine like terms: -156851.0439876 + 63500 = -93351.0439876 x2 = -93351.0439876 Simplifying x2 = -93351.0439876 Reorder the terms: 93351.0439876 + x2 = -93351.0439876 + 93351.0439876 Combine like terms: -93351.0439876 + 93351.0439876 = 0.0000000 93351.0439876 + x2 = 0.0000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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