x^2+13x+31=1

Solution for x^2+13x+31=1 equation:

Simplifying
x2 + 13x + 31 = 1

Reorder the terms:
31 + 13x + x2 = 1

Solving
31 + 13x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
31 + -1 + 13x + x2 = 1 + -1

Combine like terms: 31 + -1 = 30
30 + 13x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
30 + 13x + x2 = 0

Factor a trinomial.
(10 + x)(3 + x) = 0

Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-10, -3}