4x^4-5x^2-1=0

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Solution for 4x^4-5x^2-1=0 equation: 


Simplifying
4x4 + -5x2 + -1 = 0

Reorder the terms:
-1 + -5x2 + 4x4 = 0

Solving
-1 + -5x2 + 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'.
-0.25 + -1.25x2 + x4 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.25x2 + 0.25 + x4 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.25x2 + x4 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.25x2 + x4 = 0 + 0.25
-1.25x2 + x4 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.25x2 + x4 = 0.25

The x term is -1.25x2.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x2 + 0.390625 + x4 = 0.25 + 0.390625

Reorder the terms:
0.390625 + -1.25x2 + x4 = 0.25 + 0.390625

Combine like terms: 0.25 + 0.390625 = 0.640625
0.390625 + -1.25x2 + x4 = 0.640625

Factor a perfect square on the left side:
(x2 + -0.625)(x2 + -0.625) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x2 + -0.625) equal to 0.80039053 and -0.80039053.


Subproblem 1
x2 + -0.625 = 0.80039053

Simplifying
x2 + -0.625 = 0.80039053

Reorder the terms:
-0.625 + x2 = 0.80039053

Solving
-0.625 + x2 = 0.80039053

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x2 = 0.80039053 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x2 = 0.80039053 + 0.625
x2 = 0.80039053 + 0.625

Combine like terms: 0.80039053 + 0.625 = 1.42539053
x2 = 1.42539053

Simplifying
x2 = 1.42539053

Take the square root of each side:
x = {-1.193897202, 1.193897202}


Subproblem 2
x2 + -0.625 = -0.80039053

Simplifying
x2 + -0.625 = -0.80039053

Reorder the terms:
-0.625 + x2 = -0.80039053

Solving
-0.625 + x2 = -0.80039053

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x2 = -0.80039053 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x2 = -0.80039053 + 0.625
x2 = -0.80039053 + 0.625

Combine like terms: -0.80039053 + 0.625 = -0.17539053
x2 = -0.17539053

Simplifying
x2 = -0.17539053

Reorder the terms:
0.17539053 + x2 = -0.17539053 + 0.17539053

Combine like terms: -0.17539053 + 0.17539053 = 0.00000000
0.17539053 + 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.

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