2x^4-8x^2+6=x^2+2

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Solution for 2x^4-8x^2+6=x^2+2 equation: 


Simplifying
2x4 + -8x2 + 6 = x2 + 2

Reorder the terms:
6 + -8x2 + 2x4 = x2 + 2

Reorder the terms:
6 + -8x2 + 2x4 = 2 + x2

Solving
6 + -8x2 + 2x4 = 2 + x2

Solving for variable 'x'.

Reorder the terms:
6 + -2 + -8x2 + -1x2 + 2x4 = 2 + x2 + -2 + -1x2

Combine like terms: 6 + -2 = 4
4 + -8x2 + -1x2 + 2x4 = 2 + x2 + -2 + -1x2

Combine like terms: -8x2 + -1x2 = -9x2
4 + -9x2 + 2x4 = 2 + x2 + -2 + -1x2

Reorder the terms:
4 + -9x2 + 2x4 = 2 + -2 + x2 + -1x2

Combine like terms: 2 + -2 = 0
4 + -9x2 + 2x4 = 0 + x2 + -1x2
4 + -9x2 + 2x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -9x2 + 2x4 = 0

Factor a trinomial.
(1 + -2x2)(4 + -1x2) = 0

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


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

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}

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 = {-0.707106781, 0.707106781, -2, 2}

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