y^4-15y^2-15=0

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Solution for y^4-15y^2-15=0 equation: 


Simplifying
y4 + -15y2 + -15 = 0

Reorder the terms:
-15 + -15y2 + y4 = 0

Solving
-15 + -15y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -15y2 + 15 + y4 = 0 + 15

Reorder the terms:
-15 + 15 + -15y2 + y4 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -15y2 + y4 = 0 + 15
-15y2 + y4 = 0 + 15

Combine like terms: 0 + 15 = 15
-15y2 + y4 = 15

The y term is -15y2.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15y2 + 56.25 + y4 = 15 + 56.25

Reorder the terms:
56.25 + -15y2 + y4 = 15 + 56.25

Combine like terms: 15 + 56.25 = 71.25
56.25 + -15y2 + y4 = 71.25

Factor a perfect square on the left side:
(y2 + -7.5)(y2 + -7.5) = 71.25

Calculate the square root of the right side: 8.440971508

Break this problem into two subproblems by setting 
(y2 + -7.5) equal to 8.440971508 and -8.440971508.


Subproblem 1
y2 + -7.5 = 8.440971508

Simplifying
y2 + -7.5 = 8.440971508

Reorder the terms:
-7.5 + y2 = 8.440971508

Solving
-7.5 + y2 = 8.440971508

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y2 = 8.440971508 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y2 = 8.440971508 + 7.5
y2 = 8.440971508 + 7.5

Combine like terms: 8.440971508 + 7.5 = 15.940971508
y2 = 15.940971508

Simplifying
y2 = 15.940971508

Take the square root of each side:
y = {-3.992614621, 3.992614621}


Subproblem 2
y2 + -7.5 = -8.440971508

Simplifying
y2 + -7.5 = -8.440971508

Reorder the terms:
-7.5 + y2 = -8.440971508

Solving
-7.5 + y2 = -8.440971508

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y2 = -8.440971508 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y2 = -8.440971508 + 7.5
y2 = -8.440971508 + 7.5

Combine like terms: -8.440971508 + 7.5 = -0.940971508
y2 = -0.940971508

Simplifying
y2 = -0.940971508

Reorder the terms:
0.940971508 + y2 = -0.940971508 + 0.940971508

Combine like terms: -0.940971508 + 0.940971508 = 0.000000000
0.940971508 + 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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