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Simplifying x4 + -120000x2 + -200000000000 = 0 Reorder the terms: -200000000000 + -120000x2 + x4 = 0 Solving -200000000000 + -120000x2 + 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 + -120000x2 + 200000000000 + x4 = 0 + 200000000000 Reorder the terms: -200000000000 + 200000000000 + -120000x2 + x4 = 0 + 200000000000 Combine like terms: -200000000000 + 200000000000 = 0 0 + -120000x2 + x4 = 0 + 200000000000 -120000x2 + x4 = 0 + 200000000000 Combine like terms: 0 + 200000000000 = 200000000000 -120000x2 + x4 = 200000000000 The x term is -120000x2. Take half its coefficient (-60000). Square it (3600000000) and add it to both sides. Add '3600000000' to each side of the equation. -120000x2 + 3600000000 + x4 = 200000000000 + 3600000000 Reorder the terms: 3600000000 + -120000x2 + x4 = 200000000000 + 3600000000 Combine like terms: 200000000000 + 3600000000 = 203600000000 3600000000 + -120000x2 + x4 = 203600000000 Factor a perfect square on the left side: (x2 + -60000)(x2 + -60000) = 203600000000 Calculate the square root of the right side: 451220.566907139 Break this problem into two subproblems by setting (x2 + -60000) equal to 451220.566907139 and -451220.566907139.Subproblem 1
x2 + -60000 = 451220.566907139 Simplifying x2 + -60000 = 451220.566907139 Reorder the terms: -60000 + x2 = 451220.566907139 Solving -60000 + x2 = 451220.566907139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60000' to each side of the equation. -60000 + 60000 + x2 = 451220.566907139 + 60000 Combine like terms: -60000 + 60000 = 0 0 + x2 = 451220.566907139 + 60000 x2 = 451220.566907139 + 60000 Combine like terms: 451220.566907139 + 60000 = 511220.566907139 x2 = 511220.566907139 Simplifying x2 = 511220.566907139 Take the square root of each side: x = {-714.996899928, 714.996899928}Subproblem 2
x2 + -60000 = -451220.566907139 Simplifying x2 + -60000 = -451220.566907139 Reorder the terms: -60000 + x2 = -451220.566907139 Solving -60000 + x2 = -451220.566907139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60000' to each side of the equation. -60000 + 60000 + x2 = -451220.566907139 + 60000 Combine like terms: -60000 + 60000 = 0 0 + x2 = -451220.566907139 + 60000 x2 = -451220.566907139 + 60000 Combine like terms: -451220.566907139 + 60000 = -391220.566907139 x2 = -391220.566907139 Simplifying x2 = -391220.566907139 Reorder the terms: 391220.566907139 + x2 = -391220.566907139 + 391220.566907139 Combine like terms: -391220.566907139 + 391220.566907139 = 0.000000000 391220.566907139 + 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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