x^4*0.0000031-x^2*0.000000616-1=0

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Solution for x^4*0.0000031-x^2*0.000000616-1=0 equation: 


Simplifying
x4 * 0.0000031 + -1x2 * 0.000000616 + -1 = 0

Reorder the terms for easier multiplication:
0.0000031x4 + -1x2 * 0.000000616 + -1 = 0

Reorder the terms for easier multiplication:
0.0000031x4 + -1 * 0.000000616x2 + -1 = 0

Multiply -1 * 0.000000616
0.0000031x4 + -0.000000616x2 + -1 = 0

Reorder the terms:
-1 + -0.000000616x2 + 0.0000031x4 = 0

Solving
-1 + -0.000000616x2 + 0.0000031x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0000031 the coefficient of the squared term: 

Divide each side by '0.0000031'.
-322580.6452 + -0.1987096774x2 + x4 = 0

Move the constant term to the right:

Add '322580.6452' to each side of the equation.
-322580.6452 + -0.1987096774x2 + 322580.6452 + x4 = 0 + 322580.6452

Reorder the terms:
-322580.6452 + 322580.6452 + -0.1987096774x2 + x4 = 0 + 322580.6452

Combine like terms: -322580.6452 + 322580.6452 = 0.0000
0.0000 + -0.1987096774x2 + x4 = 0 + 322580.6452
-0.1987096774x2 + x4 = 0 + 322580.6452

Combine like terms: 0 + 322580.6452 = 322580.6452
-0.1987096774x2 + x4 = 322580.6452

The x term is -0.1987096774x2.  Take half its coefficient (-0.0993548387).
Square it (0.009871383973) and add it to both sides.

Add '0.009871383973' to each side of the equation.
-0.1987096774x2 + 0.009871383973 + x4 = 322580.6452 + 0.009871383973

Reorder the terms:
0.009871383973 + -0.1987096774x2 + x4 = 322580.6452 + 0.009871383973

Combine like terms: 322580.6452 + 0.009871383973 = 322580.655071383973
0.009871383973 + -0.1987096774x2 + x4 = 322580.655071383973

Factor a perfect square on the left side:
(x2 + -0.0993548387)(x2 + -0.0993548387) = 322580.655071383973

Calculate the square root of the right side: 567.961842971

Break this problem into two subproblems by setting 
(x2 + -0.0993548387) equal to 567.961842971 and -567.961842971.


Subproblem 1
x2 + -0.0993548387 = 567.961842971

Simplifying
x2 + -0.0993548387 = 567.961842971

Reorder the terms:
-0.0993548387 + x2 = 567.961842971

Solving
-0.0993548387 + x2 = 567.961842971

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0993548387' to each side of the equation.
-0.0993548387 + 0.0993548387 + x2 = 567.961842971 + 0.0993548387

Combine like terms: -0.0993548387 + 0.0993548387 = 0.0000000000
0.0000000000 + x2 = 567.961842971 + 0.0993548387
x2 = 567.961842971 + 0.0993548387

Combine like terms: 567.961842971 + 0.0993548387 = 568.0611978097
x2 = 568.0611978097

Simplifying
x2 = 568.0611978097

Take the square root of each side:
x = {-23.834034443, 23.834034443}


Subproblem 2
x2 + -0.0993548387 = -567.961842971

Simplifying
x2 + -0.0993548387 = -567.961842971

Reorder the terms:
-0.0993548387 + x2 = -567.961842971

Solving
-0.0993548387 + x2 = -567.961842971

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0993548387' to each side of the equation.
-0.0993548387 + 0.0993548387 + x2 = -567.961842971 + 0.0993548387

Combine like terms: -0.0993548387 + 0.0993548387 = 0.0000000000
0.0000000000 + x2 = -567.961842971 + 0.0993548387
x2 = -567.961842971 + 0.0993548387

Combine like terms: -567.961842971 + 0.0993548387 = -567.8624881323
x2 = -567.8624881323

Simplifying
x2 = -567.8624881323

Reorder the terms:
567.8624881323 + x2 = -567.8624881323 + 567.8624881323

Combine like terms: -567.8624881323 + 567.8624881323 = 0.0000000000
567.8624881323 + x2 = 0.0000000000

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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