y^4-40y^2-256=0

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Solution for y^4-40y^2-256=0 equation: 


Simplifying
y4 + -40y2 + -256 = 0

Reorder the terms:
-256 + -40y2 + y4 = 0

Solving
-256 + -40y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + -40y2 + 256 + y4 = 0 + 256

Reorder the terms:
-256 + 256 + -40y2 + y4 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + -40y2 + y4 = 0 + 256
-40y2 + y4 = 0 + 256

Combine like terms: 0 + 256 = 256
-40y2 + y4 = 256

The y term is -40y2.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40y2 + 400 + y4 = 256 + 400

Reorder the terms:
400 + -40y2 + y4 = 256 + 400

Combine like terms: 256 + 400 = 656
400 + -40y2 + y4 = 656

Factor a perfect square on the left side:
(y2 + -20)(y2 + -20) = 656

Calculate the square root of the right side: 25.61249695

Break this problem into two subproblems by setting 
(y2 + -20) equal to 25.61249695 and -25.61249695.


Subproblem 1
y2 + -20 = 25.61249695

Simplifying
y2 + -20 = 25.61249695

Reorder the terms:
-20 + y2 = 25.61249695

Solving
-20 + y2 = 25.61249695

Solving for variable 'y'.

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

Add '20' to each side of the equation.
-20 + 20 + y2 = 25.61249695 + 20

Combine like terms: -20 + 20 = 0
0 + y2 = 25.61249695 + 20
y2 = 25.61249695 + 20

Combine like terms: 25.61249695 + 20 = 45.61249695
y2 = 45.61249695

Simplifying
y2 = 45.61249695

Take the square root of each side:
y = {-6.753702462, 6.753702462}


Subproblem 2
y2 + -20 = -25.61249695

Simplifying
y2 + -20 = -25.61249695

Reorder the terms:
-20 + y2 = -25.61249695

Solving
-20 + y2 = -25.61249695

Solving for variable 'y'.

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

Add '20' to each side of the equation.
-20 + 20 + y2 = -25.61249695 + 20

Combine like terms: -20 + 20 = 0
0 + y2 = -25.61249695 + 20
y2 = -25.61249695 + 20

Combine like terms: -25.61249695 + 20 = -5.61249695
y2 = -5.61249695

Simplifying
y2 = -5.61249695

Reorder the terms:
5.61249695 + y2 = -5.61249695 + 5.61249695

Combine like terms: -5.61249695 + 5.61249695 = 0.00000000
5.61249695 + 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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