4.25x^4-5=12

Solution for 4.25x^4-5=12 equation:

Simplifying
4.25x4 + -5 = 12

Reorder the terms:
-5 + 4.25x4 = 12

Solving
-5 + 4.25x4 = 12

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + 4.25x4 = 12 + 5

Combine like terms: -5 + 5 = 0
0 + 4.25x4 = 12 + 5
4.25x4 = 12 + 5

Combine like terms: 12 + 5 = 17
4.25x4 = 17

Divide each side by '4.25'.
x4 = 4

Simplifying
x4 = 4

Reorder the terms:
-4 + x4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + x4 = 0

Factor a difference between two squares.
(2 + x2)(-2 + x2) = 0

Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve:

Simplifying
2 + x2 = 0

Solving
2 + x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 0 + -2
x2 = 0 + -2

Combine like terms: 0 + -2 = -2
x2 = -2

Simplifying
x2 = -2

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 '(-2 + x2)' equal to zero and attempt to solve:

Simplifying
-2 + x2 = 0

Solving
-2 + x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = 0 + 2
x2 = 0 + 2

Combine like terms: 0 + 2 = 2
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-1.414213562, 1.414213562}