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Simplifying x4 + -12000x2 + -200000000000 = 0 Reorder the terms: -200000000000 + -12000x2 + x4 = 0 Solving -200000000000 + -12000x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200000000000' to each side of the equation. -200000000000 + -12000x2 + 200000000000 + x4 = 0 + 200000000000 Reorder the terms: -200000000000 + 200000000000 + -12000x2 + x4 = 0 + 200000000000 Combine like terms: -200000000000 + 200000000000 = 0 0 + -12000x2 + x4 = 0 + 200000000000 -12000x2 + x4 = 0 + 200000000000 Combine like terms: 0 + 200000000000 = 200000000000 -12000x2 + x4 = 200000000000 The x term is -12000x2. Take half its coefficient (-6000). Square it (36000000) and add it to both sides. Add '36000000' to each side of the equation. -12000x2 + 36000000 + x4 = 200000000000 + 36000000 Reorder the terms: 36000000 + -12000x2 + x4 = 200000000000 + 36000000 Combine like terms: 200000000000 + 36000000 = 200036000000 36000000 + -12000x2 + x4 = 200036000000 Factor a perfect square on the left side: (x2 + -6000)(x2 + -6000) = 200036000000 Calculate the square root of the right side: 447253.842912501 Break this problem into two subproblems by setting (x2 + -6000) equal to 447253.842912501 and -447253.842912501.Subproblem 1
x2 + -6000 = 447253.842912501 Simplifying x2 + -6000 = 447253.842912501 Reorder the terms: -6000 + x2 = 447253.842912501 Solving -6000 + x2 = 447253.842912501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x2 = 447253.842912501 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x2 = 447253.842912501 + 6000 x2 = 447253.842912501 + 6000 Combine like terms: 447253.842912501 + 6000 = 453253.842912501 x2 = 453253.842912501 Simplifying x2 = 453253.842912501 Take the square root of each side: x = {-673.241296203, 673.241296203}Subproblem 2
x2 + -6000 = -447253.842912501 Simplifying x2 + -6000 = -447253.842912501 Reorder the terms: -6000 + x2 = -447253.842912501 Solving -6000 + x2 = -447253.842912501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x2 = -447253.842912501 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x2 = -447253.842912501 + 6000 x2 = -447253.842912501 + 6000 Combine like terms: -447253.842912501 + 6000 = -441253.842912501 x2 = -441253.842912501 Simplifying x2 = -441253.842912501 Reorder the terms: 441253.842912501 + x2 = -441253.842912501 + 441253.842912501 Combine like terms: -441253.842912501 + 441253.842912501 = 0.000000000 441253.842912501 + x2 = 0.000000000 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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