0=37X^2-9X^4+4

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Solution for 0=37X^2-9X^4+4 equation: 


Simplifying
0 = 37X2 + -9X4 + 4

Reorder the terms:
0 = 4 + 37X2 + -9X4

Solving
0 = 4 + 37X2 + -9X4

Solving for variable 'X'.

Combine like terms: 0 + -4 = -4
-4 + -37X2 + 9X4 = 4 + 37X2 + -9X4 + -4 + -37X2 + 9X4

Reorder the terms:
-4 + -37X2 + 9X4 = 4 + -4 + 37X2 + -37X2 + -9X4 + 9X4

Combine like terms: 4 + -4 = 0
-4 + -37X2 + 9X4 = 0 + 37X2 + -37X2 + -9X4 + 9X4
-4 + -37X2 + 9X4 = 37X2 + -37X2 + -9X4 + 9X4

Combine like terms: 37X2 + -37X2 = 0
-4 + -37X2 + 9X4 = 0 + -9X4 + 9X4
-4 + -37X2 + 9X4 = -9X4 + 9X4

Combine like terms: -9X4 + 9X4 = 0
-4 + -37X2 + 9X4 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-0.4444444444 + -4.111111111X2 + X4 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -4.111111111X2 + 0.4444444444 + X4 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -4.111111111X2 + X4 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -4.111111111X2 + X4 = 0 + 0.4444444444
-4.111111111X2 + X4 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-4.111111111X2 + X4 = 0.4444444444

The X term is -4.111111111X2.  Take half its coefficient (-2.055555556).
Square it (4.225308644) and add it to both sides.

Add '4.225308644' to each side of the equation.
-4.111111111X2 + 4.225308644 + X4 = 0.4444444444 + 4.225308644

Reorder the terms:
4.225308644 + -4.111111111X2 + X4 = 0.4444444444 + 4.225308644

Combine like terms: 0.4444444444 + 4.225308644 = 4.6697530884
4.225308644 + -4.111111111X2 + X4 = 4.6697530884

Factor a perfect square on the left side:
(X2 + -2.055555556)(X2 + -2.055555556) = 4.6697530884

Calculate the square root of the right side: 2.160961149

Break this problem into two subproblems by setting 
(X2 + -2.055555556) equal to 2.160961149 and -2.160961149.


Subproblem 1
X2 + -2.055555556 = 2.160961149

Simplifying
X2 + -2.055555556 = 2.160961149

Reorder the terms:
-2.055555556 + X2 = 2.160961149

Solving
-2.055555556 + X2 = 2.160961149

Solving for variable 'X'.

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

Add '2.055555556' to each side of the equation.
-2.055555556 + 2.055555556 + X2 = 2.160961149 + 2.055555556

Combine like terms: -2.055555556 + 2.055555556 = 0.000000000
0.000000000 + X2 = 2.160961149 + 2.055555556
X2 = 2.160961149 + 2.055555556

Combine like terms: 2.160961149 + 2.055555556 = 4.216516705
X2 = 4.216516705

Simplifying
X2 = 4.216516705

Take the square root of each side:
X = {-2.053415863, 2.053415863}


Subproblem 2
X2 + -2.055555556 = -2.160961149

Simplifying
X2 + -2.055555556 = -2.160961149

Reorder the terms:
-2.055555556 + X2 = -2.160961149

Solving
-2.055555556 + X2 = -2.160961149

Solving for variable 'X'.

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

Add '2.055555556' to each side of the equation.
-2.055555556 + 2.055555556 + X2 = -2.160961149 + 2.055555556

Combine like terms: -2.055555556 + 2.055555556 = 0.000000000
0.000000000 + X2 = -2.160961149 + 2.055555556
X2 = -2.160961149 + 2.055555556

Combine like terms: -2.160961149 + 2.055555556 = -0.105405593
X2 = -0.105405593

Simplifying
X2 = -0.105405593

Reorder the terms:
0.105405593 + X2 = -0.105405593 + 0.105405593

Combine like terms: -0.105405593 + 0.105405593 = 0.000000000
0.105405593 + 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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