x^4+4x^2+6=10

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Solution for x^4+4x^2+6=10 equation: 


Simplifying
x4 + 4x2 + 6 = 10

Reorder the terms:
6 + 4x2 + x4 = 10

Solving
6 + 4x2 + x4 = 10

Solving for variable 'x'.

Reorder the terms:
6 + -10 + 4x2 + x4 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 4x2 + x4 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 4x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4x2 + 4 + x4 = 0 + 4

Reorder the terms:
-4 + 4 + 4x2 + x4 = 0 + 4

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

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

The x term is 4x2.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x2 + 4 + x4 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4x2 + x4 = 8

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x2 + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
x2 + 2 = 2.828427125

Simplifying
x2 + 2 = 2.828427125

Reorder the terms:
2 + x2 = 2.828427125

Solving
2 + x2 = 2.828427125

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 2.828427125 + -2
x2 = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
x2 = 0.828427125

Simplifying
x2 = 0.828427125

Take the square root of each side:
x = {-0.910179721, 0.910179721}


Subproblem 2
x2 + 2 = -2.828427125

Simplifying
x2 + 2 = -2.828427125

Reorder the terms:
2 + x2 = -2.828427125

Solving
2 + x2 = -2.828427125

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x2 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = -2.828427125 + -2
x2 = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
x2 = -4.828427125

Simplifying
x2 = -4.828427125

Reorder the terms:
4.828427125 + x2 = -4.828427125 + 4.828427125

Combine like terms: -4.828427125 + 4.828427125 = 0.000000000
4.828427125 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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