16x^4+12x^2-8=0

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Solution for 16x^4+12x^2-8=0 equation: 


Simplifying
16x4 + 12x2 + -8 = 0

Reorder the terms:
-8 + 12x2 + 16x4 = 0

Solving
-8 + 12x2 + 16x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 3x2 + 4x4) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + 3x2 + 4x4)' equal to zero and attempt to solve:

Simplifying
-2 + 3x2 + 4x4 = 0

Solving
-2 + 3x2 + 4x4 = 0

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

Divide each side by '4'.
-0.5 + 0.75x2 + x4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.75x2 + 0.5 + x4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.75x2 + x4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.75x2 + x4 = 0 + 0.5
0.75x2 + x4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.75x2 + x4 = 0.5

The x term is 0.75x2.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x2 + 0.140625 + x4 = 0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x2 + x4 = 0.5 + 0.140625

Combine like terms: 0.5 + 0.140625 = 0.640625
0.140625 + 0.75x2 + x4 = 0.640625

Factor a perfect square on the left side:
(x2 + 0.375)(x2 + 0.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x2 + 0.375) equal to 0.80039053 and -0.80039053.


Subproblem 1
x2 + 0.375 = 0.80039053

Simplifying
x2 + 0.375 = 0.80039053

Reorder the terms:
0.375 + x2 = 0.80039053

Solving
0.375 + x2 = 0.80039053

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = 0.80039053 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = 0.80039053 + -0.375
x2 = 0.80039053 + -0.375

Combine like terms: 0.80039053 + -0.375 = 0.42539053
x2 = 0.42539053

Simplifying
x2 = 0.42539053

Take the square root of each side:
x = {-0.652219695, 0.652219695}


Subproblem 2
x2 + 0.375 = -0.80039053

Simplifying
x2 + 0.375 = -0.80039053

Reorder the terms:
0.375 + x2 = -0.80039053

Solving
0.375 + x2 = -0.80039053

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = -0.80039053 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = -0.80039053 + -0.375
x2 = -0.80039053 + -0.375

Combine like terms: -0.80039053 + -0.375 = -1.17539053
x2 = -1.17539053

Simplifying
x2 = -1.17539053

Reorder the terms:
1.17539053 + x2 = -1.17539053 + 1.17539053

Combine like terms: -1.17539053 + 1.17539053 = 0.00000000
1.17539053 + x2 = 0.00000000

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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