x^4-20x^2=64

Solution for x^4-20x^2=64 equation:

Simplifying
x4 + -20x2 = 64

Reorder the terms:
-20x2 + x4 = 64

Solving
-20x2 + x4 = 64

Solving for variable 'x'.

Reorder the terms:
-64 + -20x2 + x4 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + -20x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -20x2 + 64 + x4 = 0 + 64

Reorder the terms:
-64 + 64 + -20x2 + x4 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -20x2 + x4 = 0 + 64
-20x2 + x4 = 0 + 64

Combine like terms: 0 + 64 = 64
-20x2 + x4 = 64

The x term is -20x2.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x2 + 100 + x4 = 64 + 100

Reorder the terms:
100 + -20x2 + x4 = 64 + 100

Combine like terms: 64 + 100 = 164
100 + -20x2 + x4 = 164

Factor a perfect square on the left side:
(x2 + -10)(x2 + -10) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(x2 + -10) equal to 12.806248475 and -12.806248475.

Subproblem 1
x2 + -10 = 12.806248475

Simplifying
x2 + -10 = 12.806248475

Reorder the terms:
-10 + x2 = 12.806248475

Solving
-10 + x2 = 12.806248475

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x2 = 12.806248475 + 10

Combine like terms: -10 + 10 = 0
0 + x2 = 12.806248475 + 10
x2 = 12.806248475 + 10

Combine like terms: 12.806248475 + 10 = 22.806248475
x2 = 22.806248475

Simplifying
x2 = 22.806248475

Take the square root of each side:
x = {-4.775588809, 4.775588809}

Subproblem 2
x2 + -10 = -12.806248475

Simplifying
x2 + -10 = -12.806248475

Reorder the terms:
-10 + x2 = -12.806248475

Solving
-10 + x2 = -12.806248475

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x2 = -12.806248475 + 10

Combine like terms: -10 + 10 = 0
0 + x2 = -12.806248475 + 10
x2 = -12.806248475 + 10

Combine like terms: -12.806248475 + 10 = -2.806248475
x2 = -2.806248475

Simplifying
x2 = -2.806248475

Reorder the terms:
2.806248475 + x2 = -2.806248475 + 2.806248475

Combine like terms: -2.806248475 + 2.806248475 = 0.000000000
2.806248475 + 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.