x^4-18=11x^2

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Solution for x^4-18=11x^2 equation: 


Simplifying
x4 + -18 = 11x2

Reorder the terms:
-18 + x4 = 11x2

Solving
-18 + x4 = 11x2

Solving for variable 'x'.

Reorder the terms:
-18 + -11x2 + x4 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
-18 + -11x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -11x2 + 18 + x4 = 0 + 18

Reorder the terms:
-18 + 18 + -11x2 + x4 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -11x2 + x4 = 0 + 18
-11x2 + x4 = 0 + 18

Combine like terms: 0 + 18 = 18
-11x2 + x4 = 18

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 = 18 + 30.25

Reorder the terms:
30.25 + -11x2 + x4 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + -11x2 + x4 = 48.25

Factor a perfect square on the left side:
(x2 + -5.5)(x2 + -5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x2 + -5.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x2 + -5.5 = 6.946221995

Simplifying
x2 + -5.5 = 6.946221995

Reorder the terms:
-5.5 + x2 = 6.946221995

Solving
-5.5 + x2 = 6.946221995

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 = 6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = 6.946221995 + 5.5
x2 = 6.946221995 + 5.5

Combine like terms: 6.946221995 + 5.5 = 12.446221995
x2 = 12.446221995

Simplifying
x2 = 12.446221995

Take the square root of each side:
x = {-3.52792035, 3.52792035}


Subproblem 2
x2 + -5.5 = -6.946221995

Simplifying
x2 + -5.5 = -6.946221995

Reorder the terms:
-5.5 + x2 = -6.946221995

Solving
-5.5 + x2 = -6.946221995

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 = -6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = -6.946221995 + 5.5
x2 = -6.946221995 + 5.5

Combine like terms: -6.946221995 + 5.5 = -1.446221995
x2 = -1.446221995

Simplifying
x2 = -1.446221995

Reorder the terms:
1.446221995 + x2 = -1.446221995 + 1.446221995

Combine like terms: -1.446221995 + 1.446221995 = 0.000000000
1.446221995 + 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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