(18x^4)-8x^2=2

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Solution for (18x^4)-8x^2=2 equation: 


Simplifying
(18x4) + -8x2 = 2

Reorder the terms:
-8x2 + (18x4) = 2

Solving
-8x2 + (18x4) = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -8x2 + (18x4) = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -8x2 + (18x4) = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4x2 + (9x4)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -4x2 + (9x4))' equal to zero and attempt to solve:

Simplifying
-1 + -4x2 + (9x4) = 0

Solving
-1 + -4x2 + (9x4) = 0

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

Divide each side by '9'.
-0.1111111111 + -0.4444444444x2 + x4 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.4444444444x2 + 0.1111111111 + x4 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.4444444444x2 + x4 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.4444444444x2 + x4 = 0 + 0.1111111111
-0.4444444444x2 + x4 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.4444444444x2 + x4 = 0.1111111111

The x term is -0.4444444444x2.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x2 + 0.04938271604 + x4 = 0.1111111111 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x2 + x4 = 0.1111111111 + 0.04938271604

Combine like terms: 0.1111111111 + 0.04938271604 = 0.16049382714
0.04938271604 + -0.4444444444x2 + x4 = 0.16049382714

Factor a perfect square on the left side:
((x2) + -0.2222222222)((x2) + -0.2222222222) = 0.16049382714

Calculate the square root of the right side: 0.400616808

Break this problem into two subproblems by setting 
((x2) + -0.2222222222) equal to 0.400616808 and -0.400616808.


Subproblem 1
(x2) + -0.2222222222 = 0.400616808

Simplifying
(x2) + -0.2222222222 = 0.400616808
x2 + -0.2222222222 = 0.400616808

Reorder the terms:
-0.2222222222 + x2 = 0.400616808

Solving
-0.2222222222 + x2 = 0.400616808

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x2 = 0.400616808 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x2 = 0.400616808 + 0.2222222222
x2 = 0.400616808 + 0.2222222222

Combine like terms: 0.400616808 + 0.2222222222 = 0.6228390302
x2 = 0.6228390302

Simplifying
x2 = 0.6228390302

Take the square root of each side:
x = {-0.789201514, 0.789201514}


Subproblem 2
(x2) + -0.2222222222 = -0.400616808

Simplifying
(x2) + -0.2222222222 = -0.400616808
x2 + -0.2222222222 = -0.400616808

Reorder the terms:
-0.2222222222 + x2 = -0.400616808

Solving
-0.2222222222 + x2 = -0.400616808

Solving for variable 'x'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + x2 = -0.400616808 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x2 = -0.400616808 + 0.2222222222
x2 = -0.400616808 + 0.2222222222

Combine like terms: -0.400616808 + 0.2222222222 = -0.1783945858
x2 = -0.1783945858

Simplifying
x2 = -0.1783945858

Reorder the terms:
0.1783945858 + x2 = -0.1783945858 + 0.1783945858

Combine like terms: -0.1783945858 + 0.1783945858 = 0.0000000000
0.1783945858 + x2 = 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.

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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