y^4-y^2-1152=0

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Solution for y^4-y^2-1152=0 equation: 


Simplifying
y4 + -1y2 + -1152 = 0

Reorder the terms:
-1152 + -1y2 + y4 = 0

Solving
-1152 + -1y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1152' to each side of the equation.
-1152 + -1y2 + 1152 + y4 = 0 + 1152

Reorder the terms:
-1152 + 1152 + -1y2 + y4 = 0 + 1152

Combine like terms: -1152 + 1152 = 0
0 + -1y2 + y4 = 0 + 1152
-1y2 + y4 = 0 + 1152

Combine like terms: 0 + 1152 = 1152
-1y2 + y4 = 1152

The y term is -1y2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y2 + 0.25 + y4 = 1152 + 0.25

Reorder the terms:
0.25 + -1y2 + y4 = 1152 + 0.25

Combine like terms: 1152 + 0.25 = 1152.25
0.25 + -1y2 + y4 = 1152.25

Factor a perfect square on the left side:
(y2 + -0.5)(y2 + -0.5) = 1152.25

Calculate the square root of the right side: 33.944808145

Break this problem into two subproblems by setting 
(y2 + -0.5) equal to 33.944808145 and -33.944808145.


Subproblem 1
y2 + -0.5 = 33.944808145

Simplifying
y2 + -0.5 = 33.944808145

Reorder the terms:
-0.5 + y2 = 33.944808145

Solving
-0.5 + y2 = 33.944808145

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y2 = 33.944808145 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y2 = 33.944808145 + 0.5
y2 = 33.944808145 + 0.5

Combine like terms: 33.944808145 + 0.5 = 34.444808145
y2 = 34.444808145

Simplifying
y2 = 34.444808145

Take the square root of each side:
y = {-5.868969939, 5.868969939}


Subproblem 2
y2 + -0.5 = -33.944808145

Simplifying
y2 + -0.5 = -33.944808145

Reorder the terms:
-0.5 + y2 = -33.944808145

Solving
-0.5 + y2 = -33.944808145

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y2 = -33.944808145 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y2 = -33.944808145 + 0.5
y2 = -33.944808145 + 0.5

Combine like terms: -33.944808145 + 0.5 = -33.444808145
y2 = -33.444808145

Simplifying
y2 = -33.444808145

Reorder the terms:
33.444808145 + y2 = -33.444808145 + 33.444808145

Combine like terms: -33.444808145 + 33.444808145 = 0.000000000
33.444808145 + 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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