y^4-36y^2+1.024=0

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Solution for y^4-36y^2+1.024=0 equation: 


Simplifying
y4 + -36y2 + 1.024 = 0

Reorder the terms:
1.024 + -36y2 + y4 = 0

Solving
1.024 + -36y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-1.024' to each side of the equation.
1.024 + -36y2 + -1.024 + y4 = 0 + -1.024

Reorder the terms:
1.024 + -1.024 + -36y2 + y4 = 0 + -1.024

Combine like terms: 1.024 + -1.024 = 0.000
0.000 + -36y2 + y4 = 0 + -1.024
-36y2 + y4 = 0 + -1.024

Combine like terms: 0 + -1.024 = -1.024
-36y2 + y4 = -1.024

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 = -1.024 + 324

Reorder the terms:
324 + -36y2 + y4 = -1.024 + 324

Combine like terms: -1.024 + 324 = 322.976
324 + -36y2 + y4 = 322.976

Factor a perfect square on the left side:
(y2 + -18)(y2 + -18) = 322.976

Calculate the square root of the right side: 17.971533045

Break this problem into two subproblems by setting 
(y2 + -18) equal to 17.971533045 and -17.971533045.


Subproblem 1
y2 + -18 = 17.971533045

Simplifying
y2 + -18 = 17.971533045

Reorder the terms:
-18 + y2 = 17.971533045

Solving
-18 + y2 = 17.971533045

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 = 17.971533045 + 18

Combine like terms: -18 + 18 = 0
0 + y2 = 17.971533045 + 18
y2 = 17.971533045 + 18

Combine like terms: 17.971533045 + 18 = 35.971533045
y2 = 35.971533045

Simplifying
y2 = 35.971533045

Take the square root of each side:
y = {-5.997627285, 5.997627285}


Subproblem 2
y2 + -18 = -17.971533045

Simplifying
y2 + -18 = -17.971533045

Reorder the terms:
-18 + y2 = -17.971533045

Solving
-18 + y2 = -17.971533045

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 = -17.971533045 + 18

Combine like terms: -18 + 18 = 0
0 + y2 = -17.971533045 + 18
y2 = -17.971533045 + 18

Combine like terms: -17.971533045 + 18 = 0.028466955
y2 = 0.028466955

Simplifying
y2 = 0.028466955

Take the square root of each side:
y = {-0.168721531, 0.168721531}


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-5.997627285, 5.997627285, -0.168721531, 0.168721531}

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