x^4+11x^2=10

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Solution for x^4+11x^2=10 equation: 


Simplifying
x4 + 11x2 = 10

Reorder the terms:
11x2 + x4 = 10

Solving
11x2 + x4 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 11x2 + x4 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 11x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 11x2 + 10 + x4 = 0 + 10

Reorder the terms:
-10 + 10 + 11x2 + x4 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 11x2 + x4 = 0 + 10
11x2 + x4 = 0 + 10

Combine like terms: 0 + 10 = 10
11x2 + x4 = 10

The x term is 11x2.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x2 + 30.25 + x4 = 10 + 30.25

Reorder the terms:
30.25 + 11x2 + x4 = 10 + 30.25

Combine like terms: 10 + 30.25 = 40.25
30.25 + 11x2 + x4 = 40.25

Factor a perfect square on the left side:
(x2 + 5.5)(x2 + 5.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x2 + 5.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x2 + 5.5 = 6.34428877

Simplifying
x2 + 5.5 = 6.34428877

Reorder the terms:
5.5 + x2 = 6.34428877

Solving
5.5 + x2 = 6.34428877

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x2 = 6.34428877 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = 6.34428877 + -5.5
x2 = 6.34428877 + -5.5

Combine like terms: 6.34428877 + -5.5 = 0.84428877
x2 = 0.84428877

Simplifying
x2 = 0.84428877

Take the square root of each side:
x = {-0.918851876, 0.918851876}


Subproblem 2
x2 + 5.5 = -6.34428877

Simplifying
x2 + 5.5 = -6.34428877

Reorder the terms:
5.5 + x2 = -6.34428877

Solving
5.5 + x2 = -6.34428877

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x2 = -6.34428877 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x2 = -6.34428877 + -5.5
x2 = -6.34428877 + -5.5

Combine like terms: -6.34428877 + -5.5 = -11.84428877
x2 = -11.84428877

Simplifying
x2 = -11.84428877

Reorder the terms:
11.84428877 + x2 = -11.84428877 + 11.84428877

Combine like terms: -11.84428877 + 11.84428877 = 0.00000000
11.84428877 + x2 = 0.00000000

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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