y^4+41y^2+9=0

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Solution for y^4+41y^2+9=0 equation: 


Simplifying
y4 + 41y2 + 9 = 0

Reorder the terms:
9 + 41y2 + y4 = 0

Solving
9 + 41y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 41y2 + -9 + y4 = 0 + -9

Reorder the terms:
9 + -9 + 41y2 + y4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 41y2 + y4 = 0 + -9
41y2 + y4 = 0 + -9

Combine like terms: 0 + -9 = -9
41y2 + y4 = -9

The y term is 41y2.  Take half its coefficient (20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
41y2 + 420.25 + y4 = -9 + 420.25

Reorder the terms:
420.25 + 41y2 + y4 = -9 + 420.25

Combine like terms: -9 + 420.25 = 411.25
420.25 + 41y2 + y4 = 411.25

Factor a perfect square on the left side:
(y2 + 20.5)(y2 + 20.5) = 411.25

Calculate the square root of the right side: 20.279299791

Break this problem into two subproblems by setting 
(y2 + 20.5) equal to 20.279299791 and -20.279299791.


Subproblem 1
y2 + 20.5 = 20.279299791

Simplifying
y2 + 20.5 = 20.279299791

Reorder the terms:
20.5 + y2 = 20.279299791

Solving
20.5 + y2 = 20.279299791

Solving for variable 'y'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + y2 = 20.279299791 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + y2 = 20.279299791 + -20.5
y2 = 20.279299791 + -20.5

Combine like terms: 20.279299791 + -20.5 = -0.220700209
y2 = -0.220700209

Simplifying
y2 = -0.220700209

Reorder the terms:
0.220700209 + y2 = -0.220700209 + 0.220700209

Combine like terms: -0.220700209 + 0.220700209 = 0.000000000
0.220700209 + y2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
y2 + 20.5 = -20.279299791

Simplifying
y2 + 20.5 = -20.279299791

Reorder the terms:
20.5 + y2 = -20.279299791

Solving
20.5 + y2 = -20.279299791

Solving for variable 'y'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + y2 = -20.279299791 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + y2 = -20.279299791 + -20.5
y2 = -20.279299791 + -20.5

Combine like terms: -20.279299791 + -20.5 = -40.779299791
y2 = -40.779299791

Simplifying
y2 = -40.779299791

Reorder the terms:
40.779299791 + y2 = -40.779299791 + 40.779299791

Combine like terms: -40.779299791 + 40.779299791 = 0.000000000
40.779299791 + 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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