[-(y^4-y^2+1)-(y^4+7y^2+1)]+(9y^4-3y^2-11)=

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Solution for [-(y^4-y^2+1)-(y^4+7y^2+1)]+(9y^4-3y^2-11)= equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 7y2 + 1)] + (9y4 + -3y2 + -11) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 7y2 + 1)] + (9y4 + -3y2 + -11) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 7y2 + 1)] + (9y4 + -3y2 + -11) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 7y2 + 1)] + (9y4 + -3y2 + -11) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 7y2 + y4)] + (9y4 + -3y2 + -11) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 7y2 * -1 + y4 * -1)] + (9y4 + -3y2 + -11) = 0
[-1 + 1y2 + -1y4 + (-1 + -7y2 + -1y4)] + (9y4 + -3y2 + -11) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -7y2 + -1y4 + -1y4] + (9y4 + -3y2 + -11) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -7y2 + -1y4 + -1y4] + (9y4 + -3y2 + -11) = 0

Combine like terms: 1y2 + -7y2 = -6y2
[-2 + -6y2 + -1y4 + -1y4] + (9y4 + -3y2 + -11) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -6y2 + -2y4] + (9y4 + -3y2 + -11) = 0

Remove brackets around [-2 + -6y2 + -2y4]
-2 + -6y2 + -2y4 + (9y4 + -3y2 + -11) = 0

Reorder the terms:
-2 + -6y2 + -2y4 + (-11 + -3y2 + 9y4) = 0

Remove parenthesis around (-11 + -3y2 + 9y4)
-2 + -6y2 + -2y4 + -11 + -3y2 + 9y4 = 0

Reorder the terms:
-2 + -11 + -6y2 + -3y2 + -2y4 + 9y4 = 0

Combine like terms: -2 + -11 = -13
-13 + -6y2 + -3y2 + -2y4 + 9y4 = 0

Combine like terms: -6y2 + -3y2 = -9y2
-13 + -9y2 + -2y4 + 9y4 = 0

Combine like terms: -2y4 + 9y4 = 7y4
-13 + -9y2 + 7y4 = 0

Solving
-13 + -9y2 + 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'.
-1.857142857 + -1.285714286y2 + y4 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + -1.285714286y2 + 1.857142857 + y4 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + -1.285714286y2 + y4 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + -1.285714286y2 + y4 = 0 + 1.857142857
-1.285714286y2 + y4 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
-1.285714286y2 + y4 = 1.857142857

The y term is -1.285714286y2.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286y2 + 0.4132653063 + y4 = 1.857142857 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286y2 + y4 = 1.857142857 + 0.4132653063

Combine like terms: 1.857142857 + 0.4132653063 = 2.2704081633
0.4132653063 + -1.285714286y2 + y4 = 2.2704081633

Factor a perfect square on the left side:
(y2 + -0.642857143)(y2 + -0.642857143) = 2.2704081633

Calculate the square root of the right side: 1.506787365

Break this problem into two subproblems by setting 
(y2 + -0.642857143) equal to 1.506787365 and -1.506787365.


Subproblem 1
y2 + -0.642857143 = 1.506787365

Simplifying
y2 + -0.642857143 = 1.506787365

Reorder the terms:
-0.642857143 + y2 = 1.506787365

Solving
-0.642857143 + y2 = 1.506787365

Solving for variable 'y'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + y2 = 1.506787365 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + y2 = 1.506787365 + 0.642857143
y2 = 1.506787365 + 0.642857143

Combine like terms: 1.506787365 + 0.642857143 = 2.149644508
y2 = 2.149644508

Simplifying
y2 = 2.149644508

Take the square root of each side:
y = {-1.466166603, 1.466166603}


Subproblem 2
y2 + -0.642857143 = -1.506787365

Simplifying
y2 + -0.642857143 = -1.506787365

Reorder the terms:
-0.642857143 + y2 = -1.506787365

Solving
-0.642857143 + y2 = -1.506787365

Solving for variable 'y'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + y2 = -1.506787365 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + y2 = -1.506787365 + 0.642857143
y2 = -1.506787365 + 0.642857143

Combine like terms: -1.506787365 + 0.642857143 = -0.863930222
y2 = -0.863930222

Simplifying
y2 = -0.863930222

Reorder the terms:
0.863930222 + y2 = -0.863930222 + 0.863930222

Combine like terms: -0.863930222 + 0.863930222 = 0.000000000
0.863930222 + 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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