=b^4+1.909859317*b^2-8.594366927

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Solution for =b^4+1.909859317*b^2-8.594366927 equation: 


Simplifying
0 = b4 + 1.909859317b2 + -8.594366927

Reorder the terms:
0 = -8.594366927 + 1.909859317b2 + b4

Solving
0 = -8.594366927 + 1.909859317b2 + b4

Solving for variable 'b'.

Combine like terms: 0 + 8.594366927 = 8.594366927
8.594366927 + -1.909859317b2 + -1b4 = -8.594366927 + 1.909859317b2 + b4 + 8.594366927 + -1.909859317b2 + -1b4

Reorder the terms:
8.594366927 + -1.909859317b2 + -1b4 = -8.594366927 + 8.594366927 + 1.909859317b2 + -1.909859317b2 + b4 + -1b4

Combine like terms: -8.594366927 + 8.594366927 = 0.000000000
8.594366927 + -1.909859317b2 + -1b4 = 0.000000000 + 1.909859317b2 + -1.909859317b2 + b4 + -1b4
8.594366927 + -1.909859317b2 + -1b4 = 1.909859317b2 + -1.909859317b2 + b4 + -1b4

Combine like terms: 1.909859317b2 + -1.909859317b2 = 0.000000000
8.594366927 + -1.909859317b2 + -1b4 = 0.000000000 + b4 + -1b4
8.594366927 + -1.909859317b2 + -1b4 = b4 + -1b4

Combine like terms: b4 + -1b4 = 0
8.594366927 + -1.909859317b2 + -1b4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8.594366927 + 1.909859317b2 + b4 = 0

Move the constant term to the right:

Add '8.594366927' to each side of the equation.
-8.594366927 + 1.909859317b2 + 8.594366927 + b4 = 0 + 8.594366927

Reorder the terms:
-8.594366927 + 8.594366927 + 1.909859317b2 + b4 = 0 + 8.594366927

Combine like terms: -8.594366927 + 8.594366927 = 0.000000000
0.000000000 + 1.909859317b2 + b4 = 0 + 8.594366927
1.909859317b2 + b4 = 0 + 8.594366927

Combine like terms: 0 + 8.594366927 = 8.594366927
1.909859317b2 + b4 = 8.594366927

The b term is 1.909859317b2.  Take half its coefficient (0.9549296585).
Square it (0.9118906527) and add it to both sides.

Add '0.9118906527' to each side of the equation.
1.909859317b2 + 0.9118906527 + b4 = 8.594366927 + 0.9118906527

Reorder the terms:
0.9118906527 + 1.909859317b2 + b4 = 8.594366927 + 0.9118906527

Combine like terms: 8.594366927 + 0.9118906527 = 9.5062575797
0.9118906527 + 1.909859317b2 + b4 = 9.5062575797

Factor a perfect square on the left side:
(b2 + 0.9549296585)(b2 + 0.9549296585) = 9.5062575797

Calculate the square root of the right side: 3.083221948

Break this problem into two subproblems by setting 
(b2 + 0.9549296585) equal to 3.083221948 and -3.083221948.


Subproblem 1
b2 + 0.9549296585 = 3.083221948

Simplifying
b2 + 0.9549296585 = 3.083221948

Reorder the terms:
0.9549296585 + b2 = 3.083221948

Solving
0.9549296585 + b2 = 3.083221948

Solving for variable 'b'.

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

Add '-0.9549296585' to each side of the equation.
0.9549296585 + -0.9549296585 + b2 = 3.083221948 + -0.9549296585

Combine like terms: 0.9549296585 + -0.9549296585 = 0.0000000000
0.0000000000 + b2 = 3.083221948 + -0.9549296585
b2 = 3.083221948 + -0.9549296585

Combine like terms: 3.083221948 + -0.9549296585 = 2.1282922895
b2 = 2.1282922895

Simplifying
b2 = 2.1282922895

Take the square root of each side:
b = {-1.458866783, 1.458866783}


Subproblem 2
b2 + 0.9549296585 = -3.083221948

Simplifying
b2 + 0.9549296585 = -3.083221948

Reorder the terms:
0.9549296585 + b2 = -3.083221948

Solving
0.9549296585 + b2 = -3.083221948

Solving for variable 'b'.

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

Add '-0.9549296585' to each side of the equation.
0.9549296585 + -0.9549296585 + b2 = -3.083221948 + -0.9549296585

Combine like terms: 0.9549296585 + -0.9549296585 = 0.0000000000
0.0000000000 + b2 = -3.083221948 + -0.9549296585
b2 = -3.083221948 + -0.9549296585

Combine like terms: -3.083221948 + -0.9549296585 = -4.0381516065
b2 = -4.0381516065

Simplifying
b2 = -4.0381516065

Reorder the terms:
4.0381516065 + b2 = -4.0381516065 + 4.0381516065

Combine like terms: -4.0381516065 + 4.0381516065 = 0.0000000000
4.0381516065 + 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.

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