y^4+21y^2+100=0

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Solution for y^4+21y^2+100=0 equation: 


Simplifying
y4 + 21y2 + 100 = 0

Reorder the terms:
100 + 21y2 + y4 = 0

Solving
100 + 21y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 21y2 + -100 + y4 = 0 + -100

Reorder the terms:
100 + -100 + 21y2 + y4 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 21y2 + y4 = 0 + -100
21y2 + y4 = 0 + -100

Combine like terms: 0 + -100 = -100
21y2 + y4 = -100

The y term is 21y2.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21y2 + 110.25 + y4 = -100 + 110.25

Reorder the terms:
110.25 + 21y2 + y4 = -100 + 110.25

Combine like terms: -100 + 110.25 = 10.25
110.25 + 21y2 + y4 = 10.25

Factor a perfect square on the left side:
(y2 + 10.5)(y2 + 10.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(y2 + 10.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
y2 + 10.5 = 3.201562119

Simplifying
y2 + 10.5 = 3.201562119

Reorder the terms:
10.5 + y2 = 3.201562119

Solving
10.5 + y2 = 3.201562119

Solving for variable 'y'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + y2 = 3.201562119 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y2 = 3.201562119 + -10.5
y2 = 3.201562119 + -10.5

Combine like terms: 3.201562119 + -10.5 = -7.298437881
y2 = -7.298437881

Simplifying
y2 = -7.298437881

Reorder the terms:
7.298437881 + y2 = -7.298437881 + 7.298437881

Combine like terms: -7.298437881 + 7.298437881 = 0.000000000
7.298437881 + 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 + 10.5 = -3.201562119

Simplifying
y2 + 10.5 = -3.201562119

Reorder the terms:
10.5 + y2 = -3.201562119

Solving
10.5 + y2 = -3.201562119

Solving for variable 'y'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + y2 = -3.201562119 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y2 = -3.201562119 + -10.5
y2 = -3.201562119 + -10.5

Combine like terms: -3.201562119 + -10.5 = -13.701562119
y2 = -13.701562119

Simplifying
y2 = -13.701562119

Reorder the terms:
13.701562119 + y2 = -13.701562119 + 13.701562119

Combine like terms: -13.701562119 + 13.701562119 = 0.000000000
13.701562119 + 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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