0=256x^4+50x^2-81

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Solution for 0=256x^4+50x^2-81 equation: 


Simplifying
0 = 256x4 + 50x2 + -81

Reorder the terms:
0 = -81 + 50x2 + 256x4

Solving
0 = -81 + 50x2 + 256x4

Solving for variable 'x'.

Combine like terms: 0 + 81 = 81
81 + -50x2 + -256x4 = -81 + 50x2 + 256x4 + 81 + -50x2 + -256x4

Reorder the terms:
81 + -50x2 + -256x4 = -81 + 81 + 50x2 + -50x2 + 256x4 + -256x4

Combine like terms: -81 + 81 = 0
81 + -50x2 + -256x4 = 0 + 50x2 + -50x2 + 256x4 + -256x4
81 + -50x2 + -256x4 = 50x2 + -50x2 + 256x4 + -256x4

Combine like terms: 50x2 + -50x2 = 0
81 + -50x2 + -256x4 = 0 + 256x4 + -256x4
81 + -50x2 + -256x4 = 256x4 + -256x4

Combine like terms: 256x4 + -256x4 = 0
81 + -50x2 + -256x4 = 0

Begin completing the square.  Divide all terms by
-256 the coefficient of the squared term: 

Divide each side by '-256'.
-0.31640625 + 0.1953125x2 + x4 = 0

Move the constant term to the right:

Add '0.31640625' to each side of the equation.
-0.31640625 + 0.1953125x2 + 0.31640625 + x4 = 0 + 0.31640625

Reorder the terms:
-0.31640625 + 0.31640625 + 0.1953125x2 + x4 = 0 + 0.31640625

Combine like terms: -0.31640625 + 0.31640625 = 0.00000000
0.00000000 + 0.1953125x2 + x4 = 0 + 0.31640625
0.1953125x2 + x4 = 0 + 0.31640625

Combine like terms: 0 + 0.31640625 = 0.31640625
0.1953125x2 + x4 = 0.31640625

The x term is 0.1953125x2.  Take half its coefficient (0.09765625).
Square it (0.009536743164) and add it to both sides.

Add '0.009536743164' to each side of the equation.
0.1953125x2 + 0.009536743164 + x4 = 0.31640625 + 0.009536743164

Reorder the terms:
0.009536743164 + 0.1953125x2 + x4 = 0.31640625 + 0.009536743164

Combine like terms: 0.31640625 + 0.009536743164 = 0.325942993164
0.009536743164 + 0.1953125x2 + x4 = 0.325942993164

Factor a perfect square on the left side:
(x2 + 0.09765625)(x2 + 0.09765625) = 0.325942993164

Calculate the square root of the right side: 0.570914173

Break this problem into two subproblems by setting 
(x2 + 0.09765625) equal to 0.570914173 and -0.570914173.


Subproblem 1
x2 + 0.09765625 = 0.570914173

Simplifying
x2 + 0.09765625 = 0.570914173

Reorder the terms:
0.09765625 + x2 = 0.570914173

Solving
0.09765625 + x2 = 0.570914173

Solving for variable 'x'.

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

Add '-0.09765625' to each side of the equation.
0.09765625 + -0.09765625 + x2 = 0.570914173 + -0.09765625

Combine like terms: 0.09765625 + -0.09765625 = 0.00000000
0.00000000 + x2 = 0.570914173 + -0.09765625
x2 = 0.570914173 + -0.09765625

Combine like terms: 0.570914173 + -0.09765625 = 0.473257923
x2 = 0.473257923

Simplifying
x2 = 0.473257923

Take the square root of each side:
x = {-0.687937441, 0.687937441}


Subproblem 2
x2 + 0.09765625 = -0.570914173

Simplifying
x2 + 0.09765625 = -0.570914173

Reorder the terms:
0.09765625 + x2 = -0.570914173

Solving
0.09765625 + x2 = -0.570914173

Solving for variable 'x'.

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

Add '-0.09765625' to each side of the equation.
0.09765625 + -0.09765625 + x2 = -0.570914173 + -0.09765625

Combine like terms: 0.09765625 + -0.09765625 = 0.00000000
0.00000000 + x2 = -0.570914173 + -0.09765625
x2 = -0.570914173 + -0.09765625

Combine like terms: -0.570914173 + -0.09765625 = -0.668570423
x2 = -0.668570423

Simplifying
x2 = -0.668570423

Reorder the terms:
0.668570423 + x2 = -0.668570423 + 0.668570423

Combine like terms: -0.668570423 + 0.668570423 = 0.000000000
0.668570423 + 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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