48x^4-27=0

Solution for 48x^4-27=0 equation:

Simplifying
48x4 + -27 = 0

Reorder the terms:
-27 + 48x4 = 0

Solving
-27 + 48x4 = 0

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + 48x4 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 48x4 = 0 + 27
48x4 = 0 + 27

Combine like terms: 0 + 27 = 27
48x4 = 27

Divide each side by '48'.
x4 = 0.5625

Simplifying
x4 = 0.5625

Reorder the terms:
-0.5625 + x4 = 0.5625 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
-0.5625 + x4 = 0.0000

Factor a difference between two squares.
(0.75 + x2)(-0.75 + x2) = 0.0000

Subproblem 1
Set the factor '(0.75 + x2)' equal to zero and attempt to solve:

Simplifying
0.75 + x2 = 0

Solving
0.75 + x2 = 0

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x2 = 0 + -0.75
x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
x2 = -0.75

Simplifying
x2 = -0.75

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-0.75 + x2)' equal to zero and attempt to solve:

Simplifying
-0.75 + x2 = 0

Solving
-0.75 + x2 = 0

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x2 = 0 + 0.75
x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Solution
x = {-0.866025404, 0.866025404}