x^4-2x-19=1-2x+x^2

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Solution for x^4-2x-19=1-2x+x^2 equation: 


Simplifying
x4 + -2x + -19 = 1 + -2x + x2

Reorder the terms:
-19 + -2x + x4 = 1 + -2x + x2

Add '2x' to each side of the equation.
-19 + -2x + 2x + x4 = 1 + -2x + 2x + x2

Combine like terms: -2x + 2x = 0
-19 + 0 + x4 = 1 + -2x + 2x + x2
-19 + x4 = 1 + -2x + 2x + x2

Combine like terms: -2x + 2x = 0
-19 + x4 = 1 + 0 + x2
-19 + x4 = 1 + x2

Solving
-19 + x4 = 1 + x2

Solving for variable 'x'.

Reorder the terms:
-19 + -1 + -1x2 + x4 = 1 + x2 + -1 + -1x2

Combine like terms: -19 + -1 = -20
-20 + -1x2 + x4 = 1 + x2 + -1 + -1x2

Reorder the terms:
-20 + -1x2 + x4 = 1 + -1 + x2 + -1x2

Combine like terms: 1 + -1 = 0
-20 + -1x2 + x4 = 0 + x2 + -1x2
-20 + -1x2 + x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -1x2 + x4 = 0

Factor a trinomial.
(-4 + -1x2)(5 + -1x2) = 0


Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

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

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

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-2.236067978, 2.236067978}

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