x^4-144x^2+64=0

Solution for x^4-144x^2+64=0 equation:

Simplifying
x4 + -144x2 + 64 = 0

Reorder the terms:
64 + -144x2 + x4 = 0

Solving
64 + -144x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -144x2 + -64 + x4 = 0 + -64

Reorder the terms:
64 + -64 + -144x2 + x4 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -144x2 + x4 = 0 + -64
-144x2 + x4 = 0 + -64

Combine like terms: 0 + -64 = -64
-144x2 + x4 = -64

The x term is -144x2.  Take half its coefficient (-72).
Square it (5184) and add it to both sides.

Add '5184' to each side of the equation.
-144x2 + 5184 + x4 = -64 + 5184

Reorder the terms:
5184 + -144x2 + x4 = -64 + 5184

Combine like terms: -64 + 5184 = 5120
5184 + -144x2 + x4 = 5120

Factor a perfect square on the left side:
(x2 + -72)(x2 + -72) = 5120

Calculate the square root of the right side: 71.55417528

Break this problem into two subproblems by setting 
(x2 + -72) equal to 71.55417528 and -71.55417528.

Subproblem 1
x2 + -72 = 71.55417528

Simplifying
x2 + -72 = 71.55417528

Reorder the terms:
-72 + x2 = 71.55417528

Solving
-72 + x2 = 71.55417528

Solving for variable 'x'.

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

Add '72' to each side of the equation.
-72 + 72 + x2 = 71.55417528 + 72

Combine like terms: -72 + 72 = 0
0 + x2 = 71.55417528 + 72
x2 = 71.55417528 + 72

Combine like terms: 71.55417528 + 72 = 143.55417528
x2 = 143.55417528

Simplifying
x2 = 143.55417528

Take the square root of each side:
x = {-11.98140957, 11.98140957}

Subproblem 2
x2 + -72 = -71.55417528

Simplifying
x2 + -72 = -71.55417528

Reorder the terms:
-72 + x2 = -71.55417528

Solving
-72 + x2 = -71.55417528

Solving for variable 'x'.

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

Add '72' to each side of the equation.
-72 + 72 + x2 = -71.55417528 + 72

Combine like terms: -72 + 72 = 0
0 + x2 = -71.55417528 + 72
x2 = -71.55417528 + 72

Combine like terms: -71.55417528 + 72 = 0.44582472
x2 = 0.44582472

Simplifying
x2 = 0.44582472

Take the square root of each side:
x = {-0.667701071, 0.667701071}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-11.98140957, 11.98140957, -0.667701071, 0.667701071}