8x^4-3x^2-18=0

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Solution for 8x^4-3x^2-18=0 equation: 


Simplifying
8x4 + -3x2 + -18 = 0

Reorder the terms:
-18 + -3x2 + 8x4 = 0

Solving
-18 + -3x2 + 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'.
-2.25 + -0.375x2 + x4 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.375x2 + 2.25 + x4 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.375x2 + x4 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.375x2 + x4 = 0 + 2.25
-0.375x2 + x4 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.375x2 + x4 = 2.25

The x term is -0.375x2.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x2 + 0.03515625 + x4 = 2.25 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x2 + x4 = 2.25 + 0.03515625

Combine like terms: 2.25 + 0.03515625 = 2.28515625
0.03515625 + -0.375x2 + x4 = 2.28515625

Factor a perfect square on the left side:
(x2 + -0.1875)(x2 + -0.1875) = 2.28515625

Calculate the square root of the right side: 1.511673328

Break this problem into two subproblems by setting 
(x2 + -0.1875) equal to 1.511673328 and -1.511673328.


Subproblem 1
x2 + -0.1875 = 1.511673328

Simplifying
x2 + -0.1875 = 1.511673328

Reorder the terms:
-0.1875 + x2 = 1.511673328

Solving
-0.1875 + x2 = 1.511673328

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x2 = 1.511673328 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x2 = 1.511673328 + 0.1875
x2 = 1.511673328 + 0.1875

Combine like terms: 1.511673328 + 0.1875 = 1.699173328
x2 = 1.699173328

Simplifying
x2 = 1.699173328

Take the square root of each side:
x = {-1.303523428, 1.303523428}


Subproblem 2
x2 + -0.1875 = -1.511673328

Simplifying
x2 + -0.1875 = -1.511673328

Reorder the terms:
-0.1875 + x2 = -1.511673328

Solving
-0.1875 + x2 = -1.511673328

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x2 = -1.511673328 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x2 = -1.511673328 + 0.1875
x2 = -1.511673328 + 0.1875

Combine like terms: -1.511673328 + 0.1875 = -1.324173328
x2 = -1.324173328

Simplifying
x2 = -1.324173328

Reorder the terms:
1.324173328 + x2 = -1.324173328 + 1.324173328

Combine like terms: -1.324173328 + 1.324173328 = 0.000000000
1.324173328 + 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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