X^4+10X^2+18=0

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Solution for X^4+10X^2+18=0 equation: 


Simplifying
X4 + 10X2 + 18 = 0

Reorder the terms:
18 + 10X2 + X4 = 0

Solving
18 + 10X2 + X4 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10X2 + -18 + X4 = 0 + -18

Reorder the terms:
18 + -18 + 10X2 + X4 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10X2 + X4 = 0 + -18
10X2 + X4 = 0 + -18

Combine like terms: 0 + -18 = -18
10X2 + X4 = -18

The X term is 10X2.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10X2 + 25 + X4 = -18 + 25

Reorder the terms:
25 + 10X2 + X4 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10X2 + X4 = 7

Factor a perfect square on the left side:
(X2 + 5)(X2 + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(X2 + 5) equal to 2.645751311 and -2.645751311.


Subproblem 1
X2 + 5 = 2.645751311

Simplifying
X2 + 5 = 2.645751311

Reorder the terms:
5 + X2 = 2.645751311

Solving
5 + X2 = 2.645751311

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X2 = 2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + X2 = 2.645751311 + -5
X2 = 2.645751311 + -5

Combine like terms: 2.645751311 + -5 = -2.354248689
X2 = -2.354248689

Simplifying
X2 = -2.354248689

Reorder the terms:
2.354248689 + X2 = -2.354248689 + 2.354248689

Combine like terms: -2.354248689 + 2.354248689 = 0.000000000
2.354248689 + X2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
X2 + 5 = -2.645751311

Simplifying
X2 + 5 = -2.645751311

Reorder the terms:
5 + X2 = -2.645751311

Solving
5 + X2 = -2.645751311

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X2 = -2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + X2 = -2.645751311 + -5
X2 = -2.645751311 + -5

Combine like terms: -2.645751311 + -5 = -7.645751311
X2 = -7.645751311

Simplifying
X2 = -7.645751311

Reorder the terms:
7.645751311 + X2 = -7.645751311 + 7.645751311

Combine like terms: -7.645751311 + 7.645751311 = 0.000000000
7.645751311 + 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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