y^4+17y^2-16=0

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Solution for y^4+17y^2-16=0 equation: 


Simplifying
y4 + 17y2 + -16 = 0

Reorder the terms:
-16 + 17y2 + y4 = 0

Solving
-16 + 17y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 17y2 + 16 + y4 = 0 + 16

Reorder the terms:
-16 + 16 + 17y2 + y4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 17y2 + y4 = 0 + 16
17y2 + y4 = 0 + 16

Combine like terms: 0 + 16 = 16
17y2 + y4 = 16

The y term is 17y2.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17y2 + 72.25 + y4 = 16 + 72.25

Reorder the terms:
72.25 + 17y2 + y4 = 16 + 72.25

Combine like terms: 16 + 72.25 = 88.25
72.25 + 17y2 + y4 = 88.25

Factor a perfect square on the left side:
(y2 + 8.5)(y2 + 8.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(y2 + 8.5) equal to 9.394147114 and -9.394147114.


Subproblem 1
y2 + 8.5 = 9.394147114

Simplifying
y2 + 8.5 = 9.394147114

Reorder the terms:
8.5 + y2 = 9.394147114

Solving
8.5 + y2 = 9.394147114

Solving for variable 'y'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + y2 = 9.394147114 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + y2 = 9.394147114 + -8.5
y2 = 9.394147114 + -8.5

Combine like terms: 9.394147114 + -8.5 = 0.894147114
y2 = 0.894147114

Simplifying
y2 = 0.894147114

Take the square root of each side:
y = {-0.945593525, 0.945593525}


Subproblem 2
y2 + 8.5 = -9.394147114

Simplifying
y2 + 8.5 = -9.394147114

Reorder the terms:
8.5 + y2 = -9.394147114

Solving
8.5 + y2 = -9.394147114

Solving for variable 'y'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + y2 = -9.394147114 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + y2 = -9.394147114 + -8.5
y2 = -9.394147114 + -8.5

Combine like terms: -9.394147114 + -8.5 = -17.894147114
y2 = -17.894147114

Simplifying
y2 = -17.894147114

Reorder the terms:
17.894147114 + y2 = -17.894147114 + 17.894147114

Combine like terms: -17.894147114 + 17.894147114 = 0.000000000
17.894147114 + 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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