8x^4-2x^2-9=0

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Solution for 8x^4-2x^2-9=0 equation: 


Simplifying
8x4 + -2x2 + -9 = 0

Reorder the terms:
-9 + -2x2 + 8x4 = 0

Solving
-9 + -2x2 + 8x4 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.125 + -0.25x2 + x4 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.25x2 + 1.125 + x4 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.25x2 + x4 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.25x2 + x4 = 0 + 1.125
-0.25x2 + x4 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.25x2 + x4 = 1.125

The x term is -0.25x2.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x2 + 0.015625 + x4 = 1.125 + 0.015625

Reorder the terms:
0.015625 + -0.25x2 + x4 = 1.125 + 0.015625

Combine like terms: 1.125 + 0.015625 = 1.140625
0.015625 + -0.25x2 + x4 = 1.140625

Factor a perfect square on the left side:
(x2 + -0.125)(x2 + -0.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x2 + -0.125) equal to 1.068000468 and -1.068000468.


Subproblem 1
x2 + -0.125 = 1.068000468

Simplifying
x2 + -0.125 = 1.068000468

Reorder the terms:
-0.125 + x2 = 1.068000468

Solving
-0.125 + x2 = 1.068000468

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x2 = 1.068000468 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x2 = 1.068000468 + 0.125
x2 = 1.068000468 + 0.125

Combine like terms: 1.068000468 + 0.125 = 1.193000468
x2 = 1.193000468

Simplifying
x2 = 1.193000468

Take the square root of each side:
x = {-1.092245608, 1.092245608}


Subproblem 2
x2 + -0.125 = -1.068000468

Simplifying
x2 + -0.125 = -1.068000468

Reorder the terms:
-0.125 + x2 = -1.068000468

Solving
-0.125 + x2 = -1.068000468

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x2 = -1.068000468 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x2 = -1.068000468 + 0.125
x2 = -1.068000468 + 0.125

Combine like terms: -1.068000468 + 0.125 = -0.943000468
x2 = -0.943000468

Simplifying
x2 = -0.943000468

Reorder the terms:
0.943000468 + x2 = -0.943000468 + 0.943000468

Combine like terms: -0.943000468 + 0.943000468 = 0.000000000
0.943000468 + x2 = 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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