x^2+11x+31=1

Solution for x^2+11x+31=1 equation:

Simplifying
x2 + 11x + 31 = 1

Reorder the terms:
31 + 11x + x2 = 1

Solving
31 + 11x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
31 + -1 + 11x + x2 = 1 + -1

Combine like terms: 31 + -1 = 30
30 + 11x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
30 + 11x + x2 = 0

Factor a trinomial.
(6 + x)(5 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {-6, -5}