25y^4+y^2-1=0

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Solution for 25y^4+y^2-1=0 equation: 


Simplifying
25y4 + y2 + -1 = 0

Reorder the terms:
-1 + y2 + 25y4 = 0

Solving
-1 + y2 + 25y4 = 0

Solving for variable 'y'.

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

Divide each side by '25'.
-0.04 + 0.04y2 + y4 = 0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.04y2 + 0.04 + y4 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.04y2 + y4 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.04y2 + y4 = 0 + 0.04
0.04y2 + y4 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.04y2 + y4 = 0.04

The y term is y2.  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.
0.04y2 + 0.25 + y4 = 0.04 + 0.25

Reorder the terms:
0.25 + 0.04y2 + y4 = 0.04 + 0.25

Combine like terms: 0.04 + 0.25 = 0.29
0.25 + 0.04y2 + y4 = 0.29

Factor a perfect square on the left side:
(y2 + 0.5)(y2 + 0.5) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(y2 + 0.5) equal to 0.538516481 and -0.538516481.


Subproblem 1
y2 + 0.5 = 0.538516481

Simplifying
y2 + 0.5 = 0.538516481

Reorder the terms:
0.5 + y2 = 0.538516481

Solving
0.5 + y2 = 0.538516481

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 + y2 = 0.538516481 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y2 = 0.538516481 + -0.5
y2 = 0.538516481 + -0.5

Combine like terms: 0.538516481 + -0.5 = 0.038516481
y2 = 0.038516481

Simplifying
y2 = 0.038516481

Take the square root of each side:
y = {-0.196256162, 0.196256162}


Subproblem 2
y2 + 0.5 = -0.538516481

Simplifying
y2 + 0.5 = -0.538516481

Reorder the terms:
0.5 + y2 = -0.538516481

Solving
0.5 + y2 = -0.538516481

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 + y2 = -0.538516481 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y2 = -0.538516481 + -0.5
y2 = -0.538516481 + -0.5

Combine like terms: -0.538516481 + -0.5 = -1.038516481
y2 = -1.038516481

Simplifying
y2 = -1.038516481

Reorder the terms:
1.038516481 + y2 = -1.038516481 + 1.038516481

Combine like terms: -1.038516481 + 1.038516481 = 0.000000000
1.038516481 + y2 = 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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