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Simplifying x4 + -127000x2 + -205700000000 = 0 Reorder the terms: -205700000000 + -127000x2 + x4 = 0 Solving -205700000000 + -127000x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '205700000000' to each side of the equation. -205700000000 + -127000x2 + 205700000000 + x4 = 0 + 205700000000 Reorder the terms: -205700000000 + 205700000000 + -127000x2 + x4 = 0 + 205700000000 Combine like terms: -205700000000 + 205700000000 = 0 0 + -127000x2 + x4 = 0 + 205700000000 -127000x2 + x4 = 0 + 205700000000 Combine like terms: 0 + 205700000000 = 205700000000 -127000x2 + x4 = 205700000000 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 = 205700000000 + 4032250000 Reorder the terms: 4032250000 + -127000x2 + x4 = 205700000000 + 4032250000 Combine like terms: 205700000000 + 4032250000 = 209732250000 4032250000 + -127000x2 + x4 = 209732250000 Factor a perfect square on the left side: (x2 + -63500)(x2 + -63500) = 209732250000 Calculate the square root of the right side: 457965.337116249 Break this problem into two subproblems by setting (x2 + -63500) equal to 457965.337116249 and -457965.337116249.Subproblem 1
x2 + -63500 = 457965.337116249 Simplifying x2 + -63500 = 457965.337116249 Reorder the terms: -63500 + x2 = 457965.337116249 Solving -63500 + x2 = 457965.337116249 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 = 457965.337116249 + 63500 Combine like terms: -63500 + 63500 = 0 0 + x2 = 457965.337116249 + 63500 x2 = 457965.337116249 + 63500 Combine like terms: 457965.337116249 + 63500 = 521465.337116249 x2 = 521465.337116249 Simplifying x2 = 521465.337116249 Take the square root of each side: x = {-722.125568801, 722.125568801}Subproblem 2
x2 + -63500 = -457965.337116249 Simplifying x2 + -63500 = -457965.337116249 Reorder the terms: -63500 + x2 = -457965.337116249 Solving -63500 + x2 = -457965.337116249 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 = -457965.337116249 + 63500 Combine like terms: -63500 + 63500 = 0 0 + x2 = -457965.337116249 + 63500 x2 = -457965.337116249 + 63500 Combine like terms: -457965.337116249 + 63500 = -394465.337116249 x2 = -394465.337116249 Simplifying x2 = -394465.337116249 Reorder the terms: 394465.337116249 + x2 = -394465.337116249 + 394465.337116249 Combine like terms: -394465.337116249 + 394465.337116249 = 0.000000000 394465.337116249 + 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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