4a^4-1=0

Solution for 4a^4-1=0 equation:

Simplifying
4a4 + -1 = 0

Reorder the terms:
-1 + 4a4 = 0

Solving
-1 + 4a4 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + 4a4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4a4 = 0 + 1
4a4 = 0 + 1

Combine like terms: 0 + 1 = 1
4a4 = 1

Divide each side by '4'.
a4 = 0.25

Simplifying
a4 = 0.25

Reorder the terms:
-0.25 + a4 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + a4 = 0.00

Factor a difference between two squares.
(0.5 + a2)(-0.5 + a2) = 0.00

Subproblem 1
Set the factor '(0.5 + a2)' equal to zero and attempt to solve:

Simplifying
0.5 + a2 = 0

Solving
0.5 + a2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a2 = 0 + -0.5
a2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
a2 = -0.5

Simplifying
a2 = -0.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-0.5 + a2)' equal to zero and attempt to solve:

Simplifying
-0.5 + a2 = 0

Solving
-0.5 + a2 = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a2 = 0 + 0.5
a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
a2 = 0.5

Simplifying
a2 = 0.5

Take the square root of each side:
a = {-0.707106781, 0.707106781}
Solution
a = {-0.707106781, 0.707106781}