0=32-0.5*x^4

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Solution for 0=32-0.5*x^4 equation: 


Simplifying
0 = 32 + -0.5x4

Solving
0 = 32 + -0.5x4

Solving for variable 'x'.

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

Add '0.5x4' to each side of the equation.
0 + 0.5x4 = 32 + -0.5x4 + 0.5x4
Remove the zero:
0.5x4 = 32 + -0.5x4 + 0.5x4

Combine like terms: -0.5x4 + 0.5x4 = 0.0
0.5x4 = 32 + 0.0
0.5x4 = 32

Divide each side by '0.5'.
x4 = 64

Simplifying
x4 = 64

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

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

Factor a difference between two squares.
(8 + x2)(-8 + x2) = 0


Subproblem 1
Set the factor '(8 + x2)' equal to zero and attempt to solve:

Simplifying
8 + x2 = 0

Solving
8 + x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 0 + -8
x2 = 0 + -8

Combine like terms: 0 + -8 = -8
x2 = -8

Simplifying
x2 = -8

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 '(-8 + x2)' equal to zero and attempt to solve:

Simplifying
-8 + x2 = 0

Solving
-8 + x2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x2 = 0 + 8
x2 = 0 + 8

Combine like terms: 0 + 8 = 8
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {-2.828427125, 2.828427125}

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