0.25=y^12-y^6

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Solution for 0.25=y^12-y^6 equation: 


Simplifying
0.25 = y12 + -1y6

Reorder the terms:
0.25 = -1y6 + y12

Solving
0.25 = -1y6 + y12

Solving for variable 'y'.

Reorder the terms:
0.25 + y6 + -1y12 = -1y6 + y6 + y12 + -1y12

Combine like terms: -1y6 + y6 = 0
0.25 + y6 + -1y12 = 0 + y12 + -1y12
0.25 + y6 + -1y12 = y12 + -1y12

Combine like terms: y12 + -1y12 = 0
0.25 + y6 + -1y12 = 0

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

Divide each side by '-1'.
-0.25 + -1y6 + y12 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1y6 + 0.25 + y12 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1y6 + y12 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1y6 + y12 = 0 + 0.25
-1y6 + y12 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1y6 + y12 = 0.25

The y term is y6.  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.
-1y6 + 0.25 + y12 = 0.25 + 0.25

Reorder the terms:
0.25 + -1y6 + y12 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1y6 + y12 = 0.5

Factor a perfect square on the left side:
(y6 + 0.5)(y6 + 0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(y6 + 0.5) equal to 0.707106781 and -0.707106781.


Subproblem 1
y6 + 0.5 = 0.707106781

Simplifying
y6 + 0.5 = 0.707106781

Reorder the terms:
0.5 + y6 = 0.707106781

Solving
0.5 + y6 = 0.707106781

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y6 = 0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y6 = 0.707106781 + -0.5
y6 = 0.707106781 + -0.5

Combine like terms: 0.707106781 + -0.5 = 0.207106781
y6 = 0.207106781

Simplifying
y6 = 0.207106781

Reorder the terms:
-0.207106781 + y6 = 0.207106781 + -0.207106781

Combine like terms: 0.207106781 + -0.207106781 = 0.000000000
-0.207106781 + y6 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
y6 + 0.5 = -0.707106781

Simplifying
y6 + 0.5 = -0.707106781

Reorder the terms:
0.5 + y6 = -0.707106781

Solving
0.5 + y6 = -0.707106781

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y6 = -0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y6 = -0.707106781 + -0.5
y6 = -0.707106781 + -0.5

Combine like terms: -0.707106781 + -0.5 = -1.207106781
y6 = -1.207106781

Simplifying
y6 = -1.207106781

Reorder the terms:
1.207106781 + y6 = -1.207106781 + 1.207106781

Combine like terms: -1.207106781 + 1.207106781 = 0.000000000
1.207106781 + y6 = 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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