0=x^4-5x^2-14

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Solution for 0=x^4-5x^2-14 equation: 


Simplifying
0 = x4 + -5x2 + -14

Reorder the terms:
0 = -14 + -5x2 + x4

Solving
0 = -14 + -5x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + 5x2 + -1x4 = -14 + -5x2 + x4 + 14 + 5x2 + -1x4

Reorder the terms:
14 + 5x2 + -1x4 = -14 + 14 + -5x2 + 5x2 + x4 + -1x4

Combine like terms: -14 + 14 = 0
14 + 5x2 + -1x4 = 0 + -5x2 + 5x2 + x4 + -1x4
14 + 5x2 + -1x4 = -5x2 + 5x2 + x4 + -1x4

Combine like terms: -5x2 + 5x2 = 0
14 + 5x2 + -1x4 = 0 + x4 + -1x4
14 + 5x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
14 + 5x2 + -1x4 = 0

Factor a trinomial.
(7 + -1x2)(2 + x2) = 0


Subproblem 1
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}

Subproblem 2
Set the factor '(2 + x2)' equal to zero and attempt to solve:

Simplifying
2 + x2 = 0

Solving
2 + x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 0 + -2
x2 = 0 + -2

Combine like terms: 0 + -2 = -2
x2 = -2

Simplifying
x2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.645751311, 2.645751311}

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