x^2+10x+20=31

Solution for x^2+10x+20=31 equation:

Simplifying
x2 + 10x + 20 = 31

Reorder the terms:
20 + 10x + x2 = 31

Solving
20 + 10x + x2 = 31

Solving for variable 'x'.

Reorder the terms:
20 + -31 + 10x + x2 = 31 + -31

Combine like terms: 20 + -31 = -11
-11 + 10x + x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-11 + 10x + x2 = 0

Factor a trinomial.
(-11 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

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

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

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-11, 1}