y^4-36y^2-1296=0

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Solution for y^4-36y^2-1296=0 equation: 


Simplifying
y4 + -36y2 + -1296 = 0

Reorder the terms:
-1296 + -36y2 + y4 = 0

Solving
-1296 + -36y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1296' to each side of the equation.
-1296 + -36y2 + 1296 + y4 = 0 + 1296

Reorder the terms:
-1296 + 1296 + -36y2 + y4 = 0 + 1296

Combine like terms: -1296 + 1296 = 0
0 + -36y2 + y4 = 0 + 1296
-36y2 + y4 = 0 + 1296

Combine like terms: 0 + 1296 = 1296
-36y2 + y4 = 1296

The y term is -36y2.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36y2 + 324 + y4 = 1296 + 324

Reorder the terms:
324 + -36y2 + y4 = 1296 + 324

Combine like terms: 1296 + 324 = 1620
324 + -36y2 + y4 = 1620

Factor a perfect square on the left side:
(y2 + -18)(y2 + -18) = 1620

Calculate the square root of the right side: 40.249223595

Break this problem into two subproblems by setting 
(y2 + -18) equal to 40.249223595 and -40.249223595.


Subproblem 1
y2 + -18 = 40.249223595

Simplifying
y2 + -18 = 40.249223595

Reorder the terms:
-18 + y2 = 40.249223595

Solving
-18 + y2 = 40.249223595

Solving for variable 'y'.

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

Add '18' to each side of the equation.
-18 + 18 + y2 = 40.249223595 + 18

Combine like terms: -18 + 18 = 0
0 + y2 = 40.249223595 + 18
y2 = 40.249223595 + 18

Combine like terms: 40.249223595 + 18 = 58.249223595
y2 = 58.249223595

Simplifying
y2 = 58.249223595

Take the square root of each side:
y = {-7.632117897, 7.632117897}


Subproblem 2
y2 + -18 = -40.249223595

Simplifying
y2 + -18 = -40.249223595

Reorder the terms:
-18 + y2 = -40.249223595

Solving
-18 + y2 = -40.249223595

Solving for variable 'y'.

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

Add '18' to each side of the equation.
-18 + 18 + y2 = -40.249223595 + 18

Combine like terms: -18 + 18 = 0
0 + y2 = -40.249223595 + 18
y2 = -40.249223595 + 18

Combine like terms: -40.249223595 + 18 = -22.249223595
y2 = -22.249223595

Simplifying
y2 = -22.249223595

Reorder the terms:
22.249223595 + y2 = -22.249223595 + 22.249223595

Combine like terms: -22.249223595 + 22.249223595 = 0.000000000
22.249223595 + 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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