4x^4-44x^2+48=0

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Solution for 4x^4-44x^2+48=0 equation: 


Simplifying
4x4 + -44x2 + 48 = 0

Reorder the terms:
48 + -44x2 + 4x4 = 0

Solving
48 + -44x2 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -11x2 + x4) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(12 + -11x2 + x4)' equal to zero and attempt to solve:

Simplifying
12 + -11x2 + x4 = 0

Solving
12 + -11x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -11x2 + -12 + x4 = 0 + -12

Reorder the terms:
12 + -12 + -11x2 + x4 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -11x2 + x4 = 0 + -12
-11x2 + x4 = 0 + -12

Combine like terms: 0 + -12 = -12
-11x2 + x4 = -12

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 = -12 + 30.25

Reorder the terms:
30.25 + -11x2 + x4 = -12 + 30.25

Combine like terms: -12 + 30.25 = 18.25
30.25 + -11x2 + x4 = 18.25

Factor a perfect square on the left side:
(x2 + -5.5)(x2 + -5.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x2 + -5.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x2 + -5.5 = 4.272001873

Simplifying
x2 + -5.5 = 4.272001873

Reorder the terms:
-5.5 + x2 = 4.272001873

Solving
-5.5 + x2 = 4.272001873

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 = 4.272001873 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = 4.272001873 + 5.5
x2 = 4.272001873 + 5.5

Combine like terms: 4.272001873 + 5.5 = 9.772001873
x2 = 9.772001873

Simplifying
x2 = 9.772001873

Take the square root of each side:
x = {-3.126020133, 3.126020133}


Subproblem 2
x2 + -5.5 = -4.272001873

Simplifying
x2 + -5.5 = -4.272001873

Reorder the terms:
-5.5 + x2 = -4.272001873

Solving
-5.5 + x2 = -4.272001873

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 = -4.272001873 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x2 = -4.272001873 + 5.5
x2 = -4.272001873 + 5.5

Combine like terms: -4.272001873 + 5.5 = 1.227998127
x2 = 1.227998127

Simplifying
x2 = 1.227998127

Take the square root of each side:
x = {-1.108150769, 1.108150769}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.126020133, 3.126020133, -1.108150769, 1.108150769}
Solution
x = {-3.126020133, 3.126020133, -1.108150769, 1.108150769}

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