(0.000000000735*x^4)-(0.0714*x^2)+0.1568=0

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Solution for (0.000000000735*x^4)-(0.0714*x^2)+0.1568=0 equation: 


Simplifying
(0.000000000735x4) + -1(0.0714x2) + 0.1568 = 0

Remove parenthesis around (0.0714x2)
(0.000000000735x4) + -1 * 0.0714x2 + 0.1568 = 0

Multiply -1 * 0.0714
(0.000000000735x4) + -0.0714x2 + 0.1568 = 0

Reorder the terms:
0.1568 + -0.0714x2 + (0.000000000735x4) = 0

Solving
0.1568 + -0.0714x2 + (0.000000000735x4) = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.000000000735 the coefficient of the squared term: 

Divide each side by '0.000000000735'.
213333333.3 + -97142857.14x2 + x4 = 0

Move the constant term to the right:

Add '-213333333.3' to each side of the equation.
213333333.3 + -97142857.14x2 + -213333333.3 + x4 = 0 + -213333333.3

Reorder the terms:
213333333.3 + -213333333.3 + -97142857.14x2 + x4 = 0 + -213333333.3

Combine like terms: 213333333.3 + -213333333.3 = 0.0
0.0 + -97142857.14x2 + x4 = 0 + -213333333.3
-97142857.14x2 + x4 = 0 + -213333333.3

Combine like terms: 0 + -213333333.3 = -213333333.3
-97142857.14x2 + x4 = -213333333.3

The x term is -97142857.14x2.  Take half its coefficient (-48571428.57).
Square it (2359183673000000) and add it to both sides.

Add '2359183673000000' to each side of the equation.
-97142857.14x2 + 2359183673000000 + x4 = -213333333.3 + 2359183673000000

Reorder the terms:
2359183673000000 + -97142857.14x2 + x4 = -213333333.3 + 2359183673000000

Combine like terms: -213333333.3 + 2359183673000000 = 2359183459666666.7
2359183673000000 + -97142857.14x2 + x4 = 2359183459666666.7

Factor a perfect square on the left side:
((x2) + -48571428.57)((x2) + -48571428.57) = 2359183459666666.7

Calculate the square root of the right side: 48571426.370518158

Break this problem into two subproblems by setting 
((x2) + -48571428.57) equal to 48571426.370518158 and -48571426.370518158.


Subproblem 1
(x2) + -48571428.57 = 48571426.370518158

Simplifying
(x2) + -48571428.57 = 48571426.370518158
x2 + -48571428.57 = 48571426.370518158

Reorder the terms:
-48571428.57 + x2 = 48571426.370518158

Solving
-48571428.57 + x2 = 48571426.370518158

Solving for variable 'x'.

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

Add '48571428.57' to each side of the equation.
-48571428.57 + 48571428.57 + x2 = 48571426.370518158 + 48571428.57

Combine like terms: -48571428.57 + 48571428.57 = 0.00
0.00 + x2 = 48571426.370518158 + 48571428.57
x2 = 48571426.370518158 + 48571428.57

Combine like terms: 48571426.370518158 + 48571428.57 = 97142854.940518158
x2 = 97142854.940518158

Simplifying
x2 = 97142854.940518158

Take the square root of each side:
x = {-9856.107494367, 9856.107494367}


Subproblem 2
(x2) + -48571428.57 = -48571426.370518158

Simplifying
(x2) + -48571428.57 = -48571426.370518158
x2 + -48571428.57 = -48571426.370518158

Reorder the terms:
-48571428.57 + x2 = -48571426.370518158

Solving
-48571428.57 + x2 = -48571426.370518158

Solving for variable 'x'.

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

Add '48571428.57' to each side of the equation.
-48571428.57 + 48571428.57 + x2 = -48571426.370518158 + 48571428.57

Combine like terms: -48571428.57 + 48571428.57 = 0.00
0.00 + x2 = -48571426.370518158 + 48571428.57
x2 = -48571426.370518158 + 48571428.57

Combine like terms: -48571426.370518158 + 48571428.57 = 2.199481842
x2 = 2.199481842

Simplifying
x2 = 2.199481842

Take the square root of each side:
x = {-1.483065016, 1.483065016}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-9856.107494367, 9856.107494367, -1.483065016, 1.483065016}

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