[-(y^4-y^2+1)-(y^4+7y^2+1)]+(9y^4-4y^2-4)=

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Solution for [-(y^4-y^2+1)-(y^4+7y^2+1)]+(9y^4-4y^2-4)= equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 7y2 + 1)] + (9y4 + -4y2 + -4) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 7y2 + 1)] + (9y4 + -4y2 + -4) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 7y2 + 1)] + (9y4 + -4y2 + -4) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 7y2 + 1)] + (9y4 + -4y2 + -4) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 7y2 + y4)] + (9y4 + -4y2 + -4) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 7y2 * -1 + y4 * -1)] + (9y4 + -4y2 + -4) = 0
[-1 + 1y2 + -1y4 + (-1 + -7y2 + -1y4)] + (9y4 + -4y2 + -4) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -7y2 + -1y4 + -1y4] + (9y4 + -4y2 + -4) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -7y2 + -1y4 + -1y4] + (9y4 + -4y2 + -4) = 0

Combine like terms: 1y2 + -7y2 = -6y2
[-2 + -6y2 + -1y4 + -1y4] + (9y4 + -4y2 + -4) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -6y2 + -2y4] + (9y4 + -4y2 + -4) = 0

Remove brackets around [-2 + -6y2 + -2y4]
-2 + -6y2 + -2y4 + (9y4 + -4y2 + -4) = 0

Reorder the terms:
-2 + -6y2 + -2y4 + (-4 + -4y2 + 9y4) = 0

Remove parenthesis around (-4 + -4y2 + 9y4)
-2 + -6y2 + -2y4 + -4 + -4y2 + 9y4 = 0

Reorder the terms:
-2 + -4 + -6y2 + -4y2 + -2y4 + 9y4 = 0

Combine like terms: -2 + -4 = -6
-6 + -6y2 + -4y2 + -2y4 + 9y4 = 0

Combine like terms: -6y2 + -4y2 = -10y2
-6 + -10y2 + -2y4 + 9y4 = 0

Combine like terms: -2y4 + 9y4 = 7y4
-6 + -10y2 + 7y4 = 0

Solving
-6 + -10y2 + 7y4 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-0.8571428571 + -1.428571429y2 + y4 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -1.428571429y2 + 0.8571428571 + y4 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -1.428571429y2 + y4 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -1.428571429y2 + y4 = 0 + 0.8571428571
-1.428571429y2 + y4 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-1.428571429y2 + y4 = 0.8571428571

The y term is -1.428571429y2.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429y2 + 0.5102040819 + y4 = 0.8571428571 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429y2 + y4 = 0.8571428571 + 0.5102040819

Combine like terms: 0.8571428571 + 0.5102040819 = 1.367346939
0.5102040819 + -1.428571429y2 + y4 = 1.367346939

Factor a perfect square on the left side:
(y2 + -0.7142857145)(y2 + -0.7142857145) = 1.367346939

Calculate the square root of the right side: 1.16933611

Break this problem into two subproblems by setting 
(y2 + -0.7142857145) equal to 1.16933611 and -1.16933611.


Subproblem 1
y2 + -0.7142857145 = 1.16933611

Simplifying
y2 + -0.7142857145 = 1.16933611

Reorder the terms:
-0.7142857145 + y2 = 1.16933611

Solving
-0.7142857145 + y2 = 1.16933611

Solving for variable 'y'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + y2 = 1.16933611 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + y2 = 1.16933611 + 0.7142857145
y2 = 1.16933611 + 0.7142857145

Combine like terms: 1.16933611 + 0.7142857145 = 1.8836218245
y2 = 1.8836218245

Simplifying
y2 = 1.8836218245

Take the square root of each side:
y = {-1.372451028, 1.372451028}


Subproblem 2
y2 + -0.7142857145 = -1.16933611

Simplifying
y2 + -0.7142857145 = -1.16933611

Reorder the terms:
-0.7142857145 + y2 = -1.16933611

Solving
-0.7142857145 + y2 = -1.16933611

Solving for variable 'y'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + y2 = -1.16933611 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + y2 = -1.16933611 + 0.7142857145
y2 = -1.16933611 + 0.7142857145

Combine like terms: -1.16933611 + 0.7142857145 = -0.4550503955
y2 = -0.4550503955

Simplifying
y2 = -0.4550503955

Reorder the terms:
0.4550503955 + y2 = -0.4550503955 + 0.4550503955

Combine like terms: -0.4550503955 + 0.4550503955 = 0.0000000000
0.4550503955 + y2 = 0.0000000000

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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