x^4-37x^2=36

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Solution for x^4-37x^2=36 equation: 


Simplifying
x4 + -37x2 = 36

Reorder the terms:
-37x2 + x4 = 36

Solving
-37x2 + x4 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + -37x2 + x4 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -37x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -37x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + -37x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -37x2 + x4 = 0 + 36
-37x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
-37x2 + x4 = 36

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 = 36 + 342.25

Reorder the terms:
342.25 + -37x2 + x4 = 36 + 342.25

Combine like terms: 36 + 342.25 = 378.25
342.25 + -37x2 + x4 = 378.25

Factor a perfect square on the left side:
(x2 + -18.5)(x2 + -18.5) = 378.25

Calculate the square root of the right side: 19.448650339

Break this problem into two subproblems by setting 
(x2 + -18.5) equal to 19.448650339 and -19.448650339.


Subproblem 1
x2 + -18.5 = 19.448650339

Simplifying
x2 + -18.5 = 19.448650339

Reorder the terms:
-18.5 + x2 = 19.448650339

Solving
-18.5 + x2 = 19.448650339

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 = 19.448650339 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x2 = 19.448650339 + 18.5
x2 = 19.448650339 + 18.5

Combine like terms: 19.448650339 + 18.5 = 37.948650339
x2 = 37.948650339

Simplifying
x2 = 37.948650339

Take the square root of each side:
x = {-6.160247587, 6.160247587}


Subproblem 2
x2 + -18.5 = -19.448650339

Simplifying
x2 + -18.5 = -19.448650339

Reorder the terms:
-18.5 + x2 = -19.448650339

Solving
-18.5 + x2 = -19.448650339

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 = -19.448650339 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x2 = -19.448650339 + 18.5
x2 = -19.448650339 + 18.5

Combine like terms: -19.448650339 + 18.5 = -0.948650339
x2 = -0.948650339

Simplifying
x2 = -0.948650339

Reorder the terms:
0.948650339 + x2 = -0.948650339 + 0.948650339

Combine like terms: -0.948650339 + 0.948650339 = 0.000000000
0.948650339 + 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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