0=-310.276x^4+1804271.595x^2+350000000

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Solution for 0=-310.276x^4+1804271.595x^2+350000000 equation:


Simplifying
0 = -310.276x4 + 1804271.595x2 + 350000000

Reorder the terms:
0 = 350000000 + 1804271.595x2 + -310.276x4

Solving
0 = 350000000 + 1804271.595x2 + -310.276x4

Solving for variable 'x'.

Combine like terms: 0 + -350000000 = -350000000
-350000000 + -1804271.595x2 + 310.276x4 = 350000000 + 1804271.595x2 + -310.276x4 + -350000000 + -1804271.595x2 + 310.276x4

Reorder the terms:
-350000000 + -1804271.595x2 + 310.276x4 = 350000000 + -350000000 + 1804271.595x2 + -1804271.595x2 + -310.276x4 + 310.276x4

Combine like terms: 350000000 + -350000000 = 0
-350000000 + -1804271.595x2 + 310.276x4 = 0 + 1804271.595x2 + -1804271.595x2 + -310.276x4 + 310.276x4
-350000000 + -1804271.595x2 + 310.276x4 = 1804271.595x2 + -1804271.595x2 + -310.276x4 + 310.276x4

Combine like terms: 1804271.595x2 + -1804271.595x2 = 0.000
-350000000 + -1804271.595x2 + 310.276x4 = 0.000 + -310.276x4 + 310.276x4
-350000000 + -1804271.595x2 + 310.276x4 = -310.276x4 + 310.276x4

Combine like terms: -310.276x4 + 310.276x4 = 0.000
-350000000 + -1804271.595x2 + 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 + -5815.053678x2 + x4 = 0

Move the constant term to the right:

Add '1128027.949' to each side of the equation.
-1128027.949 + -5815.053678x2 + 1128027.949 + x4 = 0 + 1128027.949

Reorder the terms:
-1128027.949 + 1128027.949 + -5815.053678x2 + x4 = 0 + 1128027.949

Combine like terms: -1128027.949 + 1128027.949 = 0.000
0.000 + -5815.053678x2 + x4 = 0 + 1128027.949
-5815.053678x2 + x4 = 0 + 1128027.949

Combine like terms: 0 + 1128027.949 = 1128027.949
-5815.053678x2 + x4 = 1128027.949

The x term is -5815.053678x2.  Take half its coefficient (-2907.526839).
Square it (8453712.320) and add it to both sides.

Add '8453712.320' to each side of the equation.
-5815.053678x2 + 8453712.320 + x4 = 1128027.949 + 8453712.320

Reorder the terms:
8453712.320 + -5815.053678x2 + x4 = 1128027.949 + 8453712.320

Combine like terms: 1128027.949 + 8453712.320 = 9581740.269
8453712.320 + -5815.053678x2 + x4 = 9581740.269

Factor a perfect square on the left side:
(x2 + -2907.526839)(x2 + -2907.526839) = 9581740.269

Calculate the square root of the right side: 3095.438623039

Break this problem into two subproblems by setting 
(x2 + -2907.526839) equal to 3095.438623039 and -3095.438623039.

Subproblem 1

x2 + -2907.526839 = 3095.438623039 Simplifying x2 + -2907.526839 = 3095.438623039 Reorder the terms: -2907.526839 + x2 = 3095.438623039 Solving -2907.526839 + x2 = 3095.438623039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2907.526839' to each side of the equation. -2907.526839 + 2907.526839 + x2 = 3095.438623039 + 2907.526839 Combine like terms: -2907.526839 + 2907.526839 = 0.000000 0.000000 + x2 = 3095.438623039 + 2907.526839 x2 = 3095.438623039 + 2907.526839 Combine like terms: 3095.438623039 + 2907.526839 = 6002.965462039 x2 = 6002.965462039 Simplifying x2 = 6002.965462039 Take the square root of each side: x = {-77.478806535, 77.478806535}

Subproblem 2

x2 + -2907.526839 = -3095.438623039 Simplifying x2 + -2907.526839 = -3095.438623039 Reorder the terms: -2907.526839 + x2 = -3095.438623039 Solving -2907.526839 + x2 = -3095.438623039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2907.526839' to each side of the equation. -2907.526839 + 2907.526839 + x2 = -3095.438623039 + 2907.526839 Combine like terms: -2907.526839 + 2907.526839 = 0.000000 0.000000 + x2 = -3095.438623039 + 2907.526839 x2 = -3095.438623039 + 2907.526839 Combine like terms: -3095.438623039 + 2907.526839 = -187.911784039 x2 = -187.911784039 Simplifying x2 = -187.911784039 Reorder the terms: 187.911784039 + x2 = -187.911784039 + 187.911784039 Combine like terms: -187.911784039 + 187.911784039 = 0.000000000 187.911784039 + 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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