y^4-15y^2-44=0

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Solution for y^4-15y^2-44=0 equation: 


Simplifying
y4 + -15y2 + -44 = 0

Reorder the terms:
-44 + -15y2 + y4 = 0

Solving
-44 + -15y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -15y2 + 44 + y4 = 0 + 44

Reorder the terms:
-44 + 44 + -15y2 + y4 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -15y2 + y4 = 0 + 44
-15y2 + y4 = 0 + 44

Combine like terms: 0 + 44 = 44
-15y2 + y4 = 44

The y term is -15y2.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15y2 + 56.25 + y4 = 44 + 56.25

Reorder the terms:
56.25 + -15y2 + y4 = 44 + 56.25

Combine like terms: 44 + 56.25 = 100.25
56.25 + -15y2 + y4 = 100.25

Factor a perfect square on the left side:
(y2 + -7.5)(y2 + -7.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(y2 + -7.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
y2 + -7.5 = 10.012492197

Simplifying
y2 + -7.5 = 10.012492197

Reorder the terms:
-7.5 + y2 = 10.012492197

Solving
-7.5 + y2 = 10.012492197

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y2 = 10.012492197 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y2 = 10.012492197 + 7.5
y2 = 10.012492197 + 7.5

Combine like terms: 10.012492197 + 7.5 = 17.512492197
y2 = 17.512492197

Simplifying
y2 = 17.512492197

Take the square root of each side:
y = {-4.184792969, 4.184792969}


Subproblem 2
y2 + -7.5 = -10.012492197

Simplifying
y2 + -7.5 = -10.012492197

Reorder the terms:
-7.5 + y2 = -10.012492197

Solving
-7.5 + y2 = -10.012492197

Solving for variable 'y'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + y2 = -10.012492197 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y2 = -10.012492197 + 7.5
y2 = -10.012492197 + 7.5

Combine like terms: -10.012492197 + 7.5 = -2.512492197
y2 = -2.512492197

Simplifying
y2 = -2.512492197

Reorder the terms:
2.512492197 + y2 = -2.512492197 + 2.512492197

Combine like terms: -2.512492197 + 2.512492197 = 0.000000000
2.512492197 + 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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