4x^4-14x^2-3=0

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Solution for 4x^4-14x^2-3=0 equation: 


Simplifying
4x4 + -14x2 + -3 = 0

Reorder the terms:
-3 + -14x2 + 4x4 = 0

Solving
-3 + -14x2 + 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'.
-0.75 + -3.5x2 + x4 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3.5x2 + 0.75 + x4 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3.5x2 + x4 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3.5x2 + x4 = 0 + 0.75
-3.5x2 + x4 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3.5x2 + x4 = 0.75

The x term is -3.5x2.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x2 + 3.0625 + x4 = 0.75 + 3.0625

Reorder the terms:
3.0625 + -3.5x2 + x4 = 0.75 + 3.0625

Combine like terms: 0.75 + 3.0625 = 3.8125
3.0625 + -3.5x2 + x4 = 3.8125

Factor a perfect square on the left side:
(x2 + -1.75)(x2 + -1.75) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(x2 + -1.75) equal to 1.952562419 and -1.952562419.


Subproblem 1
x2 + -1.75 = 1.952562419

Simplifying
x2 + -1.75 = 1.952562419

Reorder the terms:
-1.75 + x2 = 1.952562419

Solving
-1.75 + x2 = 1.952562419

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x2 = 1.952562419 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x2 = 1.952562419 + 1.75
x2 = 1.952562419 + 1.75

Combine like terms: 1.952562419 + 1.75 = 3.702562419
x2 = 3.702562419

Simplifying
x2 = 3.702562419

Take the square root of each side:
x = {-1.92420436, 1.92420436}


Subproblem 2
x2 + -1.75 = -1.952562419

Simplifying
x2 + -1.75 = -1.952562419

Reorder the terms:
-1.75 + x2 = -1.952562419

Solving
-1.75 + x2 = -1.952562419

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x2 = -1.952562419 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x2 = -1.952562419 + 1.75
x2 = -1.952562419 + 1.75

Combine like terms: -1.952562419 + 1.75 = -0.202562419
x2 = -0.202562419

Simplifying
x2 = -0.202562419

Reorder the terms:
0.202562419 + x2 = -0.202562419 + 0.202562419

Combine like terms: -0.202562419 + 0.202562419 = 0.000000000
0.202562419 + 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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