-20x^4+21x^2+1=0

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Solution for -20x^4+21x^2+1=0 equation: 


Simplifying
-20x4 + 21x2 + 1 = 0

Reorder the terms:
1 + 21x2 + -20x4 = 0

Solving
1 + 21x2 + -20x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-0.05 + -1.05x2 + x4 = 0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -1.05x2 + 0.05 + x4 = 0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -1.05x2 + x4 = 0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -1.05x2 + x4 = 0 + 0.05
-1.05x2 + x4 = 0 + 0.05

Combine like terms: 0 + 0.05 = 0.05
-1.05x2 + x4 = 0.05

The x term is -1.05x2.  Take half its coefficient (-0.525).
Square it (0.275625) and add it to both sides.

Add '0.275625' to each side of the equation.
-1.05x2 + 0.275625 + x4 = 0.05 + 0.275625

Reorder the terms:
0.275625 + -1.05x2 + x4 = 0.05 + 0.275625

Combine like terms: 0.05 + 0.275625 = 0.325625
0.275625 + -1.05x2 + x4 = 0.325625

Factor a perfect square on the left side:
(x2 + -0.525)(x2 + -0.525) = 0.325625

Calculate the square root of the right side: 0.570635611

Break this problem into two subproblems by setting 
(x2 + -0.525) equal to 0.570635611 and -0.570635611.


Subproblem 1
x2 + -0.525 = 0.570635611

Simplifying
x2 + -0.525 = 0.570635611

Reorder the terms:
-0.525 + x2 = 0.570635611

Solving
-0.525 + x2 = 0.570635611

Solving for variable 'x'.

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

Add '0.525' to each side of the equation.
-0.525 + 0.525 + x2 = 0.570635611 + 0.525

Combine like terms: -0.525 + 0.525 = 0.000
0.000 + x2 = 0.570635611 + 0.525
x2 = 0.570635611 + 0.525

Combine like terms: 0.570635611 + 0.525 = 1.095635611
x2 = 1.095635611

Simplifying
x2 = 1.095635611

Take the square root of each side:
x = {-1.046726139, 1.046726139}


Subproblem 2
x2 + -0.525 = -0.570635611

Simplifying
x2 + -0.525 = -0.570635611

Reorder the terms:
-0.525 + x2 = -0.570635611

Solving
-0.525 + x2 = -0.570635611

Solving for variable 'x'.

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

Add '0.525' to each side of the equation.
-0.525 + 0.525 + x2 = -0.570635611 + 0.525

Combine like terms: -0.525 + 0.525 = 0.000
0.000 + x2 = -0.570635611 + 0.525
x2 = -0.570635611 + 0.525

Combine like terms: -0.570635611 + 0.525 = -0.045635611
x2 = -0.045635611

Simplifying
x2 = -0.045635611

Reorder the terms:
0.045635611 + x2 = -0.045635611 + 0.045635611

Combine like terms: -0.045635611 + 0.045635611 = 0.000000000
0.045635611 + 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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