x^2+23*x+20=0

Solution for x^2+23*x+20=0 equation:

Simplifying
x2 + 23x + 20 = 0

Reorder the terms:
20 + 23x + x2 = 0

Solving
20 + 23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 23x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 23x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 23x + x2 = 0 + -20
23x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
23x + x2 = -20

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = -20 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -20 + 132.25

Combine like terms: -20 + 132.25 = 112.25
132.25 + 23x + x2 = 112.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + 11.5) equal to 10.59481005 and -10.59481005.

Subproblem 1
x + 11.5 = 10.59481005

Simplifying
x + 11.5 = 10.59481005

Reorder the terms:
11.5 + x = 10.59481005

Solving
11.5 + x = 10.59481005

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 10.59481005 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 10.59481005 + -11.5
x = 10.59481005 + -11.5

Combine like terms: 10.59481005 + -11.5 = -0.90518995
x = -0.90518995

Simplifying
x = -0.90518995

Subproblem 2
x + 11.5 = -10.59481005

Simplifying
x + 11.5 = -10.59481005

Reorder the terms:
11.5 + x = -10.59481005

Solving
11.5 + x = -10.59481005

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -10.59481005 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -10.59481005 + -11.5
x = -10.59481005 + -11.5

Combine like terms: -10.59481005 + -11.5 = -22.09481005
x = -22.09481005

Simplifying
x = -22.09481005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.90518995, -22.09481005}