x^2+x-19=1

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

Simplifying
x2 + x + -19 = 1

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

Solving
-19 + x + x2 = 1

Solving for variable 'x'.

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

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

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

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

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

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

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

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

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

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

Simplifying
x = 4
Solution
x = {-5, 4}