8a^4-6a^2-1=0

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Solution for 8a^4-6a^2-1=0 equation: 


Simplifying
8a4 + -6a2 + -1 = 0

Reorder the terms:
-1 + -6a2 + 8a4 = 0

Solving
-1 + -6a2 + 8a4 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-0.125 + -0.75a2 + a4 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.75a2 + 0.125 + a4 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.75a2 + a4 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.75a2 + a4 = 0 + 0.125
-0.75a2 + a4 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.75a2 + a4 = 0.125

The a term is -0.75a2.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75a2 + 0.140625 + a4 = 0.125 + 0.140625

Reorder the terms:
0.140625 + -0.75a2 + a4 = 0.125 + 0.140625

Combine like terms: 0.125 + 0.140625 = 0.265625
0.140625 + -0.75a2 + a4 = 0.265625

Factor a perfect square on the left side:
(a2 + -0.375)(a2 + -0.375) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(a2 + -0.375) equal to 0.515388203 and -0.515388203.


Subproblem 1
a2 + -0.375 = 0.515388203

Simplifying
a2 + -0.375 = 0.515388203

Reorder the terms:
-0.375 + a2 = 0.515388203

Solving
-0.375 + a2 = 0.515388203

Solving for variable 'a'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + a2 = 0.515388203 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + a2 = 0.515388203 + 0.375
a2 = 0.515388203 + 0.375

Combine like terms: 0.515388203 + 0.375 = 0.890388203
a2 = 0.890388203

Simplifying
a2 = 0.890388203

Take the square root of each side:
a = {-0.943603838, 0.943603838}


Subproblem 2
a2 + -0.375 = -0.515388203

Simplifying
a2 + -0.375 = -0.515388203

Reorder the terms:
-0.375 + a2 = -0.515388203

Solving
-0.375 + a2 = -0.515388203

Solving for variable 'a'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + a2 = -0.515388203 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + a2 = -0.515388203 + 0.375
a2 = -0.515388203 + 0.375

Combine like terms: -0.515388203 + 0.375 = -0.140388203
a2 = -0.140388203

Simplifying
a2 = -0.140388203

Reorder the terms:
0.140388203 + a2 = -0.140388203 + 0.140388203

Combine like terms: -0.140388203 + 0.140388203 = 0.000000000
0.140388203 + a2 = 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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