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

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


Simplifying
4x4 + -3x2 + -8 = 0

Reorder the terms:
-8 + -3x2 + 4x4 = 0

Solving
-8 + -3x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2 + -0.75x2 + x4 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.75x2 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + -0.75x2 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.75x2 + x4 = 0 + 2
-0.75x2 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.75x2 + x4 = 2

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 = 2 + 0.140625

Reorder the terms:
0.140625 + -0.75x2 + x4 = 2 + 0.140625

Combine like terms: 2 + 0.140625 = 2.140625
0.140625 + -0.75x2 + x4 = 2.140625

Factor a perfect square on the left side:
(x2 + -0.375)(x2 + -0.375) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x2 + -0.375) equal to 1.463087489 and -1.463087489.


Subproblem 1
x2 + -0.375 = 1.463087489

Simplifying
x2 + -0.375 = 1.463087489

Reorder the terms:
-0.375 + x2 = 1.463087489

Solving
-0.375 + x2 = 1.463087489

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 = 1.463087489 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = 1.463087489 + 0.375
x2 = 1.463087489 + 0.375

Combine like terms: 1.463087489 + 0.375 = 1.838087489
x2 = 1.838087489

Simplifying
x2 = 1.838087489

Take the square root of each side:
x = {-1.355760852, 1.355760852}


Subproblem 2
x2 + -0.375 = -1.463087489

Simplifying
x2 + -0.375 = -1.463087489

Reorder the terms:
-0.375 + x2 = -1.463087489

Solving
-0.375 + x2 = -1.463087489

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 = -1.463087489 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = -1.463087489 + 0.375
x2 = -1.463087489 + 0.375

Combine like terms: -1.463087489 + 0.375 = -1.088087489
x2 = -1.088087489

Simplifying
x2 = -1.088087489

Reorder the terms:
1.088087489 + x2 = -1.088087489 + 1.088087489

Combine like terms: -1.088087489 + 1.088087489 = 0.000000000
1.088087489 + 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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