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Simplifying 0 = -310.276x4 + 1804571.595x2 + 350000000 Reorder the terms: 0 = 350000000 + 1804571.595x2 + -310.276x4 Solving 0 = 350000000 + 1804571.595x2 + -310.276x4 Solving for variable 'x'. Combine like terms: 0 + -350000000 = -350000000 -350000000 + -1804571.595x2 + 310.276x4 = 350000000 + 1804571.595x2 + -310.276x4 + -350000000 + -1804571.595x2 + 310.276x4 Reorder the terms: -350000000 + -1804571.595x2 + 310.276x4 = 350000000 + -350000000 + 1804571.595x2 + -1804571.595x2 + -310.276x4 + 310.276x4 Combine like terms: 350000000 + -350000000 = 0 -350000000 + -1804571.595x2 + 310.276x4 = 0 + 1804571.595x2 + -1804571.595x2 + -310.276x4 + 310.276x4 -350000000 + -1804571.595x2 + 310.276x4 = 1804571.595x2 + -1804571.595x2 + -310.276x4 + 310.276x4 Combine like terms: 1804571.595x2 + -1804571.595x2 = 0.000 -350000000 + -1804571.595x2 + 310.276x4 = 0.000 + -310.276x4 + 310.276x4 -350000000 + -1804571.595x2 + 310.276x4 = -310.276x4 + 310.276x4 Combine like terms: -310.276x4 + 310.276x4 = 0.000 -350000000 + -1804571.595x2 + 310.276x4 = 0.000 Begin completing the square. Divide all terms by 310.276 the coefficient of the squared term: Divide each side by '310.276'. -1128027.949 + -5816.020559x2 + x4 = 0 Move the constant term to the right: Add '1128027.949' to each side of the equation. -1128027.949 + -5816.020559x2 + 1128027.949 + x4 = 0 + 1128027.949 Reorder the terms: -1128027.949 + 1128027.949 + -5816.020559x2 + x4 = 0 + 1128027.949 Combine like terms: -1128027.949 + 1128027.949 = 0.000 0.000 + -5816.020559x2 + x4 = 0 + 1128027.949 -5816.020559x2 + x4 = 0 + 1128027.949 Combine like terms: 0 + 1128027.949 = 1128027.949 -5816.020559x2 + x4 = 1128027.949 The x term is -5816.020559x2. Take half its coefficient (-2908.01028). Square it (8456523.789) and add it to both sides. Add '8456523.789' to each side of the equation. -5816.020559x2 + 8456523.789 + x4 = 1128027.949 + 8456523.789 Reorder the terms: 8456523.789 + -5816.020559x2 + x4 = 1128027.949 + 8456523.789 Combine like terms: 1128027.949 + 8456523.789 = 9584551.738 8456523.789 + -5816.020559x2 + x4 = 9584551.738 Factor a perfect square on the left side: (x2 + -2908.01028)(x2 + -2908.01028) = 9584551.738 Calculate the square root of the right side: 3095.892720687 Break this problem into two subproblems by setting (x2 + -2908.01028) equal to 3095.892720687 and -3095.892720687.Subproblem 1
x2 + -2908.01028 = 3095.892720687 Simplifying x2 + -2908.01028 = 3095.892720687 Reorder the terms: -2908.01028 + x2 = 3095.892720687 Solving -2908.01028 + x2 = 3095.892720687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2908.01028' to each side of the equation. -2908.01028 + 2908.01028 + x2 = 3095.892720687 + 2908.01028 Combine like terms: -2908.01028 + 2908.01028 = 0.00000 0.00000 + x2 = 3095.892720687 + 2908.01028 x2 = 3095.892720687 + 2908.01028 Combine like terms: 3095.892720687 + 2908.01028 = 6003.903000687 x2 = 6003.903000687 Simplifying x2 = 6003.903000687 Take the square root of each side: x = {-77.484856589, 77.484856589}Subproblem 2
x2 + -2908.01028 = -3095.892720687 Simplifying x2 + -2908.01028 = -3095.892720687 Reorder the terms: -2908.01028 + x2 = -3095.892720687 Solving -2908.01028 + x2 = -3095.892720687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2908.01028' to each side of the equation. -2908.01028 + 2908.01028 + x2 = -3095.892720687 + 2908.01028 Combine like terms: -2908.01028 + 2908.01028 = 0.00000 0.00000 + x2 = -3095.892720687 + 2908.01028 x2 = -3095.892720687 + 2908.01028 Combine like terms: -3095.892720687 + 2908.01028 = -187.882440687 x2 = -187.882440687 Simplifying x2 = -187.882440687 Reorder the terms: 187.882440687 + x2 = -187.882440687 + 187.882440687 Combine like terms: -187.882440687 + 187.882440687 = 0.000000000 187.882440687 + 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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