27=18*x^2+x^4

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Solution for 27=18*x^2+x^4 equation: 


Simplifying
27 = 18x2 + x4

Solving
27 = 18x2 + x4

Solving for variable 'x'.

Reorder the terms:
27 + -18x2 + -1x4 = 18x2 + -18x2 + x4 + -1x4

Combine like terms: 18x2 + -18x2 = 0
27 + -18x2 + -1x4 = 0 + x4 + -1x4
27 + -18x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
27 + -18x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-27 + 18x2 + x4 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 18x2 + 27 + x4 = 0 + 27

Reorder the terms:
-27 + 27 + 18x2 + x4 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 18x2 + x4 = 0 + 27
18x2 + x4 = 0 + 27

Combine like terms: 0 + 27 = 27
18x2 + x4 = 27

The x term is 18x2.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x2 + 81 + x4 = 27 + 81

Reorder the terms:
81 + 18x2 + x4 = 27 + 81

Combine like terms: 27 + 81 = 108
81 + 18x2 + x4 = 108

Factor a perfect square on the left side:
(x2 + 9)(x2 + 9) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x2 + 9) equal to 10.392304845 and -10.392304845.


Subproblem 1
x2 + 9 = 10.392304845

Simplifying
x2 + 9 = 10.392304845

Reorder the terms:
9 + x2 = 10.392304845

Solving
9 + x2 = 10.392304845

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 10.392304845 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 10.392304845 + -9
x2 = 10.392304845 + -9

Combine like terms: 10.392304845 + -9 = 1.392304845
x2 = 1.392304845

Simplifying
x2 = 1.392304845

Take the square root of each side:
x = {-1.179959679, 1.179959679}


Subproblem 2
x2 + 9 = -10.392304845

Simplifying
x2 + 9 = -10.392304845

Reorder the terms:
9 + x2 = -10.392304845

Solving
9 + x2 = -10.392304845

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x2 = -10.392304845 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = -10.392304845 + -9
x2 = -10.392304845 + -9

Combine like terms: -10.392304845 + -9 = -19.392304845
x2 = -19.392304845

Simplifying
x2 = -19.392304845

Reorder the terms:
19.392304845 + x2 = -19.392304845 + 19.392304845

Combine like terms: -19.392304845 + 19.392304845 = 0.000000000
19.392304845 + 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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