-49+37x^2+x^4=0

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Solution for -49+37x^2+x^4=0 equation: 


Simplifying
-49 + 37x2 + x4 = 0

Solving
-49 + 37x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 37x2 + 49 + x4 = 0 + 49

Reorder the terms:
-49 + 49 + 37x2 + x4 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 37x2 + x4 = 0 + 49
37x2 + x4 = 0 + 49

Combine like terms: 0 + 49 = 49
37x2 + x4 = 49

The x term is 37x2.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x2 + 342.25 + x4 = 49 + 342.25

Reorder the terms:
342.25 + 37x2 + x4 = 49 + 342.25

Combine like terms: 49 + 342.25 = 391.25
342.25 + 37x2 + x4 = 391.25

Factor a perfect square on the left side:
(x2 + 18.5)(x2 + 18.5) = 391.25

Calculate the square root of the right side: 19.780040445

Break this problem into two subproblems by setting 
(x2 + 18.5) equal to 19.780040445 and -19.780040445.


Subproblem 1
x2 + 18.5 = 19.780040445

Simplifying
x2 + 18.5 = 19.780040445

Reorder the terms:
18.5 + x2 = 19.780040445

Solving
18.5 + x2 = 19.780040445

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x2 = 19.780040445 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x2 = 19.780040445 + -18.5
x2 = 19.780040445 + -18.5

Combine like terms: 19.780040445 + -18.5 = 1.280040445
x2 = 1.280040445

Simplifying
x2 = 1.280040445

Take the square root of each side:
x = {-1.131388724, 1.131388724}


Subproblem 2
x2 + 18.5 = -19.780040445

Simplifying
x2 + 18.5 = -19.780040445

Reorder the terms:
18.5 + x2 = -19.780040445

Solving
18.5 + x2 = -19.780040445

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x2 = -19.780040445 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x2 = -19.780040445 + -18.5
x2 = -19.780040445 + -18.5

Combine like terms: -19.780040445 + -18.5 = -38.280040445
x2 = -38.280040445

Simplifying
x2 = -38.280040445

Reorder the terms:
38.280040445 + x2 = -38.280040445 + 38.280040445

Combine like terms: -38.280040445 + 38.280040445 = 0.000000000
38.280040445 + 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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