x^4-37x^2-36=036

Solution for x^4-37x^2-36=036 equation:

Simplifying
x4 + -37x2 + -36 = 36

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

Solving
-36 + -37x2 + x4 = 36

Solving for variable 'x'.

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

Combine like terms: -36 + -36 = -72
-72 + -37x2 + x4 = 36 + -36

Combine like terms: 36 + -36 = 0
-72 + -37x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -37x2 + 72 + x4 = 0 + 72

Reorder the terms:
-72 + 72 + -37x2 + x4 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -37x2 + x4 = 0 + 72
-37x2 + x4 = 0 + 72

Combine like terms: 0 + 72 = 72
-37x2 + x4 = 72

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 = 72 + 342.25

Reorder the terms:
342.25 + -37x2 + x4 = 72 + 342.25

Combine like terms: 72 + 342.25 = 414.25
342.25 + -37x2 + x4 = 414.25

Factor a perfect square on the left side:
(x2 + -18.5)(x2 + -18.5) = 414.25

Calculate the square root of the right side: 20.353132437

Break this problem into two subproblems by setting 
(x2 + -18.5) equal to 20.353132437 and -20.353132437.

Subproblem 1
x2 + -18.5 = 20.353132437

Simplifying
x2 + -18.5 = 20.353132437

Reorder the terms:
-18.5 + x2 = 20.353132437

Solving
-18.5 + x2 = 20.353132437

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 = 20.353132437 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x2 = 20.353132437 + 18.5
x2 = 20.353132437 + 18.5

Combine like terms: 20.353132437 + 18.5 = 38.853132437
x2 = 38.853132437

Simplifying
x2 = 38.853132437

Take the square root of each side:
x = {-6.233228091, 6.233228091}

Subproblem 2
x2 + -18.5 = -20.353132437

Simplifying
x2 + -18.5 = -20.353132437

Reorder the terms:
-18.5 + x2 = -20.353132437

Solving
-18.5 + x2 = -20.353132437

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 = -20.353132437 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x2 = -20.353132437 + 18.5
x2 = -20.353132437 + 18.5

Combine like terms: -20.353132437 + 18.5 = -1.853132437
x2 = -1.853132437

Simplifying
x2 = -1.853132437

Reorder the terms:
1.853132437 + x2 = -1.853132437 + 1.853132437

Combine like terms: -1.853132437 + 1.853132437 = 0.000000000
1.853132437 + 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.