x^4=12x^2-32

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Solution for x^4=12x^2-32 equation: 


Simplifying
x4 = 12x2 + -32

Reorder the terms:
x4 = -32 + 12x2

Solving
x4 = -32 + 12x2

Solving for variable 'x'.

Reorder the terms:
32 + -12x2 + x4 = -32 + 12x2 + 32 + -12x2

Reorder the terms:
32 + -12x2 + x4 = -32 + 32 + 12x2 + -12x2

Combine like terms: -32 + 32 = 0
32 + -12x2 + x4 = 0 + 12x2 + -12x2
32 + -12x2 + x4 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
32 + -12x2 + x4 = 0

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

Factor a difference between two squares.
((2 + x)(2 + -1x))(8 + -1x2) = 0


Subproblem 1
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}

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.828427125, 2.828427125, -2, 2}

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