0.87890625-b^4=b^2

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Solution for 0.87890625-b^4=b^2 equation: 


Simplifying
0.87890625 + -1b4 = b2

Solving
0.87890625 + -1b4 = b2

Solving for variable 'b'.

Reorder the terms:
0.87890625 + -1b2 + -1b4 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
0.87890625 + -1b2 + -1b4 = 0

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

Divide each side by '-1'.
-0.87890625 + b2 + b4 = 0

Move the constant term to the right:

Add '0.87890625' to each side of the equation.
-0.87890625 + b2 + 0.87890625 + b4 = 0 + 0.87890625

Reorder the terms:
-0.87890625 + 0.87890625 + b2 + b4 = 0 + 0.87890625

Combine like terms: -0.87890625 + 0.87890625 = 0.00000000
0.00000000 + b2 + b4 = 0 + 0.87890625
b2 + b4 = 0 + 0.87890625

Combine like terms: 0 + 0.87890625 = 0.87890625
b2 + b4 = 0.87890625

The b term is b2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + b4 = 0.87890625 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b4 = 0.87890625 + 0.25

Combine like terms: 0.87890625 + 0.25 = 1.12890625
1.25 + b4 = 1.12890625

Factor a perfect square on the left side:
(b2 + 0.5)(b2 + 0.5) = 1.12890625

Calculate the square root of the right side: 1.0625

Break this problem into two subproblems by setting 
(b2 + 0.5) equal to 1.0625 and -1.0625.


Subproblem 1
b2 + 0.5 = 1.0625

Simplifying
b2 + 0.5 = 1.0625

Reorder the terms:
0.5 + b2 = 1.0625

Solving
0.5 + b2 = 1.0625

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b2 = 1.0625 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b2 = 1.0625 + -0.5
b2 = 1.0625 + -0.5

Combine like terms: 1.0625 + -0.5 = 0.5625
b2 = 0.5625

Simplifying
b2 = 0.5625

Take the square root of each side:
b = {-0.75, 0.75}


Subproblem 2
b2 + 0.5 = -1.0625

Simplifying
b2 + 0.5 = -1.0625

Reorder the terms:
0.5 + b2 = -1.0625

Solving
0.5 + b2 = -1.0625

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b2 = -1.0625 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b2 = -1.0625 + -0.5
b2 = -1.0625 + -0.5

Combine like terms: -1.0625 + -0.5 = -1.5625
b2 = -1.5625

Simplifying
b2 = -1.5625

Reorder the terms:
1.5625 + b2 = -1.5625 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
1.5625 + b2 = 0.0000

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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