y^4-32y^2-400=0

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Solution for y^4-32y^2-400=0 equation: 


Simplifying
y4 + -32y2 + -400 = 0

Reorder the terms:
-400 + -32y2 + y4 = 0

Solving
-400 + -32y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -32y2 + 400 + y4 = 0 + 400

Reorder the terms:
-400 + 400 + -32y2 + y4 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -32y2 + y4 = 0 + 400
-32y2 + y4 = 0 + 400

Combine like terms: 0 + 400 = 400
-32y2 + y4 = 400

The y term is -32y2.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32y2 + 256 + y4 = 400 + 256

Reorder the terms:
256 + -32y2 + y4 = 400 + 256

Combine like terms: 400 + 256 = 656
256 + -32y2 + y4 = 656

Factor a perfect square on the left side:
(y2 + -16)(y2 + -16) = 656

Calculate the square root of the right side: 25.61249695

Break this problem into two subproblems by setting 
(y2 + -16) equal to 25.61249695 and -25.61249695.


Subproblem 1
y2 + -16 = 25.61249695

Simplifying
y2 + -16 = 25.61249695

Reorder the terms:
-16 + y2 = 25.61249695

Solving
-16 + y2 = 25.61249695

Solving for variable 'y'.

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

Add '16' to each side of the equation.
-16 + 16 + y2 = 25.61249695 + 16

Combine like terms: -16 + 16 = 0
0 + y2 = 25.61249695 + 16
y2 = 25.61249695 + 16

Combine like terms: 25.61249695 + 16 = 41.61249695
y2 = 41.61249695

Simplifying
y2 = 41.61249695

Take the square root of each side:
y = {-6.450774911, 6.450774911}


Subproblem 2
y2 + -16 = -25.61249695

Simplifying
y2 + -16 = -25.61249695

Reorder the terms:
-16 + y2 = -25.61249695

Solving
-16 + y2 = -25.61249695

Solving for variable 'y'.

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

Add '16' to each side of the equation.
-16 + 16 + y2 = -25.61249695 + 16

Combine like terms: -16 + 16 = 0
0 + y2 = -25.61249695 + 16
y2 = -25.61249695 + 16

Combine like terms: -25.61249695 + 16 = -9.61249695
y2 = -9.61249695

Simplifying
y2 = -9.61249695

Reorder the terms:
9.61249695 + y2 = -9.61249695 + 9.61249695

Combine like terms: -9.61249695 + 9.61249695 = 0.00000000
9.61249695 + y2 = 0.00000000

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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