a^4-226a^2+256=0

Solution for a^4-226a^2+256=0 equation:

Simplifying
a4 + -226a2 + 256 = 0

Reorder the terms:
256 + -226a2 + a4 = 0

Solving
256 + -226a2 + 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 + -226a2 + -256 + a4 = 0 + -256

Reorder the terms:
256 + -256 + -226a2 + a4 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -226a2 + a4 = 0 + -256
-226a2 + a4 = 0 + -256

Combine like terms: 0 + -256 = -256
-226a2 + a4 = -256

The a term is -226a2.  Take half its coefficient (-113).
Square it (12769) and add it to both sides.

Add '12769' to each side of the equation.
-226a2 + 12769 + a4 = -256 + 12769

Reorder the terms:
12769 + -226a2 + a4 = -256 + 12769

Combine like terms: -256 + 12769 = 12513
12769 + -226a2 + a4 = 12513

Factor a perfect square on the left side:
(a2 + -113)(a2 + -113) = 12513

Calculate the square root of the right side: 111.861521534

Break this problem into two subproblems by setting 
(a2 + -113) equal to 111.861521534 and -111.861521534.

Subproblem 1
a2 + -113 = 111.861521534

Simplifying
a2 + -113 = 111.861521534

Reorder the terms:
-113 + a2 = 111.861521534

Solving
-113 + a2 = 111.861521534

Solving for variable 'a'.

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

Add '113' to each side of the equation.
-113 + 113 + a2 = 111.861521534 + 113

Combine like terms: -113 + 113 = 0
0 + a2 = 111.861521534 + 113
a2 = 111.861521534 + 113

Combine like terms: 111.861521534 + 113 = 224.861521534
a2 = 224.861521534

Simplifying
a2 = 224.861521534

Take the square root of each side:
a = {-14.995383341, 14.995383341}

Subproblem 2
a2 + -113 = -111.861521534

Simplifying
a2 + -113 = -111.861521534

Reorder the terms:
-113 + a2 = -111.861521534

Solving
-113 + a2 = -111.861521534

Solving for variable 'a'.

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

Add '113' to each side of the equation.
-113 + 113 + a2 = -111.861521534 + 113

Combine like terms: -113 + 113 = 0
0 + a2 = -111.861521534 + 113
a2 = -111.861521534 + 113

Combine like terms: -111.861521534 + 113 = 1.138478466
a2 = 1.138478466

Simplifying
a2 = 1.138478466

Take the square root of each side:
a = {-1.066995064, 1.066995064}

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-14.995383341, 14.995383341, -1.066995064, 1.066995064}