4x^4-21x^2-5=0

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Solution for 4x^4-21x^2-5=0 equation: 


Simplifying
4x4 + -21x2 + -5 = 0

Reorder the terms:
-5 + -21x2 + 4x4 = 0

Solving
-5 + -21x2 + 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'.
-1.25 + -5.25x2 + x4 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -5.25x2 + 1.25 + x4 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -5.25x2 + x4 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -5.25x2 + x4 = 0 + 1.25
-5.25x2 + x4 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-5.25x2 + x4 = 1.25

The x term is -5.25x2.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25x2 + 6.890625 + x4 = 1.25 + 6.890625

Reorder the terms:
6.890625 + -5.25x2 + x4 = 1.25 + 6.890625

Combine like terms: 1.25 + 6.890625 = 8.140625
6.890625 + -5.25x2 + x4 = 8.140625

Factor a perfect square on the left side:
(x2 + -2.625)(x2 + -2.625) = 8.140625

Calculate the square root of the right side: 2.853178053

Break this problem into two subproblems by setting 
(x2 + -2.625) equal to 2.853178053 and -2.853178053.


Subproblem 1
x2 + -2.625 = 2.853178053

Simplifying
x2 + -2.625 = 2.853178053

Reorder the terms:
-2.625 + x2 = 2.853178053

Solving
-2.625 + x2 = 2.853178053

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x2 = 2.853178053 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x2 = 2.853178053 + 2.625
x2 = 2.853178053 + 2.625

Combine like terms: 2.853178053 + 2.625 = 5.478178053
x2 = 5.478178053

Simplifying
x2 = 5.478178053

Take the square root of each side:
x = {-2.340550801, 2.340550801}


Subproblem 2
x2 + -2.625 = -2.853178053

Simplifying
x2 + -2.625 = -2.853178053

Reorder the terms:
-2.625 + x2 = -2.853178053

Solving
-2.625 + x2 = -2.853178053

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x2 = -2.853178053 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x2 = -2.853178053 + 2.625
x2 = -2.853178053 + 2.625

Combine like terms: -2.853178053 + 2.625 = -0.228178053
x2 = -0.228178053

Simplifying
x2 = -0.228178053

Reorder the terms:
0.228178053 + x2 = -0.228178053 + 0.228178053

Combine like terms: -0.228178053 + 0.228178053 = 0.000000000
0.228178053 + 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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