5x^4-64=32x^2

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Solution for 5x^4-64=32x^2 equation: 


Simplifying
5x4 + -64 = 32x2

Reorder the terms:
-64 + 5x4 = 32x2

Solving
-64 + 5x4 = 32x2

Solving for variable 'x'.

Reorder the terms:
-64 + -32x2 + 5x4 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-64 + -32x2 + 5x4 = 0

Factor a trinomial.
(-8 + -5x2)(8 + -1x2) = 0


Subproblem 1
Set the factor '(-8 + -5x2)' equal to zero and attempt to solve:

Simplifying
-8 + -5x2 = 0

Solving
-8 + -5x2 = 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 + -5x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x2 = 0 + 8
-5x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5x2 = 8

Divide each side by '-5'.
x2 = -1.6

Simplifying
x2 = -1.6

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 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
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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