12b^4-3b^2-1=0

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Solution for 12b^4-3b^2-1=0 equation: 


Simplifying
12b4 + -3b2 + -1 = 0

Reorder the terms:
-1 + -3b2 + 12b4 = 0

Solving
-1 + -3b2 + 12b4 = 0

Solving for variable 'b'.

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

Divide each side by '12'.
-0.08333333333 + -0.25b2 + b4 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.25b2 + 0.08333333333 + b4 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.25b2 + b4 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.25b2 + b4 = 0 + 0.08333333333
-0.25b2 + b4 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.25b2 + b4 = 0.08333333333

The b term is -0.25b2.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25b2 + 0.015625 + b4 = 0.08333333333 + 0.015625

Reorder the terms:
0.015625 + -0.25b2 + b4 = 0.08333333333 + 0.015625

Combine like terms: 0.08333333333 + 0.015625 = 0.09895833333
0.015625 + -0.25b2 + b4 = 0.09895833333

Factor a perfect square on the left side:
(b2 + -0.125)(b2 + -0.125) = 0.09895833333

Calculate the square root of the right side: 0.314576435

Break this problem into two subproblems by setting 
(b2 + -0.125) equal to 0.314576435 and -0.314576435.


Subproblem 1
b2 + -0.125 = 0.314576435

Simplifying
b2 + -0.125 = 0.314576435

Reorder the terms:
-0.125 + b2 = 0.314576435

Solving
-0.125 + b2 = 0.314576435

Solving for variable 'b'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + b2 = 0.314576435 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + b2 = 0.314576435 + 0.125
b2 = 0.314576435 + 0.125

Combine like terms: 0.314576435 + 0.125 = 0.439576435
b2 = 0.439576435

Simplifying
b2 = 0.439576435

Take the square root of each side:
b = {-0.663005607, 0.663005607}


Subproblem 2
b2 + -0.125 = -0.314576435

Simplifying
b2 + -0.125 = -0.314576435

Reorder the terms:
-0.125 + b2 = -0.314576435

Solving
-0.125 + b2 = -0.314576435

Solving for variable 'b'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + b2 = -0.314576435 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + b2 = -0.314576435 + 0.125
b2 = -0.314576435 + 0.125

Combine like terms: -0.314576435 + 0.125 = -0.189576435
b2 = -0.189576435

Simplifying
b2 = -0.189576435

Reorder the terms:
0.189576435 + b2 = -0.189576435 + 0.189576435

Combine like terms: -0.189576435 + 0.189576435 = 0.000000000
0.189576435 + b2 = 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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