x^4=4(x^2+8)

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Solution for x^4=4(x^2+8) equation: 


Simplifying
x4 = 4(x2 + 8)

Reorder the terms:
x4 = 4(8 + x2)
x4 = (8 * 4 + x2 * 4)
x4 = (32 + 4x2)

Solving
x4 = 32 + 4x2

Solving for variable 'x'.

Reorder the terms:
-32 + -4x2 + x4 = 32 + 4x2 + -32 + -4x2

Reorder the terms:
-32 + -4x2 + x4 = 32 + -32 + 4x2 + -4x2

Combine like terms: 32 + -32 = 0
-32 + -4x2 + x4 = 0 + 4x2 + -4x2
-32 + -4x2 + x4 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-32 + -4x2 + x4 = 0

Factor a trinomial.
(-4 + -1x2)(8 + -1x2) = 0


Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

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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