x^2-x-5=1

Solution for x^2-x-5=1 equation:

Simplifying
x2 + -1x + -5 = 1

Reorder the terms:
-5 + -1x + x2 = 1

Solving
-5 + -1x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-5 + -1 + -1x + x2 = 1 + -1

Combine like terms: -5 + -1 = -6
-6 + -1x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-6 + -1x + x2 = 0

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}