2x^4-26x^2+27=0

Solution for 2x^4-26x^2+27=0 equation:

Simplifying
2x4 + -26x2 + 27 = 0

Reorder the terms:
27 + -26x2 + 2x4 = 0

Solving
27 + -26x2 + 2x4 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
13.5 + -13x2 + x4 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -13x2 + -13.5 + x4 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -13x2 + x4 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -13x2 + x4 = 0 + -13.5
-13x2 + x4 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-13x2 + x4 = -13.5

The x term is -13x2.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x2 + 42.25 + x4 = -13.5 + 42.25

Reorder the terms:
42.25 + -13x2 + x4 = -13.5 + 42.25

Combine like terms: -13.5 + 42.25 = 28.75
42.25 + -13x2 + x4 = 28.75

Factor a perfect square on the left side:
(x2 + -6.5)(x2 + -6.5) = 28.75

Calculate the square root of the right side: 5.361902647

Break this problem into two subproblems by setting 
(x2 + -6.5) equal to 5.361902647 and -5.361902647.

Subproblem 1
x2 + -6.5 = 5.361902647

Simplifying
x2 + -6.5 = 5.361902647

Reorder the terms:
-6.5 + x2 = 5.361902647

Solving
-6.5 + x2 = 5.361902647

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x2 = 5.361902647 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x2 = 5.361902647 + 6.5
x2 = 5.361902647 + 6.5

Combine like terms: 5.361902647 + 6.5 = 11.861902647
x2 = 11.861902647

Simplifying
x2 = 11.861902647

Take the square root of each side:
x = {-3.4441113, 3.4441113}

Subproblem 2
x2 + -6.5 = -5.361902647

Simplifying
x2 + -6.5 = -5.361902647

Reorder the terms:
-6.5 + x2 = -5.361902647

Solving
-6.5 + x2 = -5.361902647

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x2 = -5.361902647 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x2 = -5.361902647 + 6.5
x2 = -5.361902647 + 6.5

Combine like terms: -5.361902647 + 6.5 = 1.138097353
x2 = 1.138097353

Simplifying
x2 = 1.138097353

Take the square root of each side:
x = {-1.066816457, 1.066816457}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.4441113, 3.4441113, -1.066816457, 1.066816457}