36b^4+30b^2-12=0

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Solution for 36b^4+30b^2-12=0 equation: 


Simplifying
36b4 + 30b2 + -12 = 0

Reorder the terms:
-12 + 30b2 + 36b4 = 0

Solving
-12 + 30b2 + 36b4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 5b2 + 6b4) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-2 + 5b2 + 6b4)' equal to zero and attempt to solve:

Simplifying
-2 + 5b2 + 6b4 = 0

Solving
-2 + 5b2 + 6b4 = 0

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

Divide each side by '6'.
-0.3333333333 + 0.8333333333b2 + b4 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.8333333333b2 + 0.3333333333 + b4 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.8333333333b2 + b4 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.8333333333b2 + b4 = 0 + 0.3333333333
0.8333333333b2 + b4 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.8333333333b2 + b4 = 0.3333333333

The b term is 0.8333333333b2.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333b2 + 0.1736111111 + b4 = 0.3333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333b2 + b4 = 0.3333333333 + 0.1736111111

Combine like terms: 0.3333333333 + 0.1736111111 = 0.5069444444
0.1736111111 + 0.8333333333b2 + b4 = 0.5069444444

Factor a perfect square on the left side:
(b2 + 0.4166666667)(b2 + 0.4166666667) = 0.5069444444

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(b2 + 0.4166666667) equal to 0.712000312 and -0.712000312.


Subproblem 1
b2 + 0.4166666667 = 0.712000312

Simplifying
b2 + 0.4166666667 = 0.712000312

Reorder the terms:
0.4166666667 + b2 = 0.712000312

Solving
0.4166666667 + b2 = 0.712000312

Solving for variable 'b'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + b2 = 0.712000312 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + b2 = 0.712000312 + -0.4166666667
b2 = 0.712000312 + -0.4166666667

Combine like terms: 0.712000312 + -0.4166666667 = 0.2953336453
b2 = 0.2953336453

Simplifying
b2 = 0.2953336453

Take the square root of each side:
b = {-0.543446083, 0.543446083}


Subproblem 2
b2 + 0.4166666667 = -0.712000312

Simplifying
b2 + 0.4166666667 = -0.712000312

Reorder the terms:
0.4166666667 + b2 = -0.712000312

Solving
0.4166666667 + b2 = -0.712000312

Solving for variable 'b'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + b2 = -0.712000312 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + b2 = -0.712000312 + -0.4166666667
b2 = -0.712000312 + -0.4166666667

Combine like terms: -0.712000312 + -0.4166666667 = -1.1286669787
b2 = -1.1286669787

Simplifying
b2 = -1.1286669787

Reorder the terms:
1.1286669787 + b2 = -1.1286669787 + 1.1286669787

Combine like terms: -1.1286669787 + 1.1286669787 = 0.0000000000
1.1286669787 + b2 = 0.0000000000

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.

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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