a^4-256a^2+256=0

Solution for a^4-256a^2+256=0 equation:

Simplifying
a4 + -256a2 + 256 = 0

Reorder the terms:
256 + -256a2 + a4 = 0

Solving
256 + -256a2 + a4 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -256a2 + -256 + a4 = 0 + -256

Reorder the terms:
256 + -256 + -256a2 + a4 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -256a2 + a4 = 0 + -256
-256a2 + a4 = 0 + -256

Combine like terms: 0 + -256 = -256
-256a2 + a4 = -256

The a term is -256a2.  Take half its coefficient (-128).
Square it (16384) and add it to both sides.

Add '16384' to each side of the equation.
-256a2 + 16384 + a4 = -256 + 16384

Reorder the terms:
16384 + -256a2 + a4 = -256 + 16384

Combine like terms: -256 + 16384 = 16128
16384 + -256a2 + a4 = 16128

Factor a perfect square on the left side:
(a2 + -128)(a2 + -128) = 16128

Calculate the square root of the right side: 126.996062931

Break this problem into two subproblems by setting 
(a2 + -128) equal to 126.996062931 and -126.996062931.

Subproblem 1
a2 + -128 = 126.996062931

Simplifying
a2 + -128 = 126.996062931

Reorder the terms:
-128 + a2 = 126.996062931

Solving
-128 + a2 = 126.996062931

Solving for variable 'a'.

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

Add '128' to each side of the equation.
-128 + 128 + a2 = 126.996062931 + 128

Combine like terms: -128 + 128 = 0
0 + a2 = 126.996062931 + 128
a2 = 126.996062931 + 128

Combine like terms: 126.996062931 + 128 = 254.996062931
a2 = 254.996062931

Simplifying
a2 = 254.996062931

Take the square root of each side:
a = {-15.968596148, 15.968596148}

Subproblem 2
a2 + -128 = -126.996062931

Simplifying
a2 + -128 = -126.996062931

Reorder the terms:
-128 + a2 = -126.996062931

Solving
-128 + a2 = -126.996062931

Solving for variable 'a'.

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

Add '128' to each side of the equation.
-128 + 128 + a2 = -126.996062931 + 128

Combine like terms: -128 + 128 = 0
0 + a2 = -126.996062931 + 128
a2 = -126.996062931 + 128

Combine like terms: -126.996062931 + 128 = 1.003937069
a2 = 1.003937069

Simplifying
a2 = 1.003937069

Take the square root of each side:
a = {-1.001966601, 1.001966601}

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-15.968596148, 15.968596148, -1.001966601, 1.001966601}