x^2+23x+124=0

Solution for x^2+23x+124=0 equation:

Simplifying
x2 + 23x + 124 = 0

Reorder the terms:
124 + 23x + x2 = 0

Solving
124 + 23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-124' to each side of the equation.
124 + 23x + -124 + x2 = 0 + -124

Reorder the terms:
124 + -124 + 23x + x2 = 0 + -124

Combine like terms: 124 + -124 = 0
0 + 23x + x2 = 0 + -124
23x + x2 = 0 + -124

Combine like terms: 0 + -124 = -124
23x + x2 = -124

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 = -124 + 132.25

Reorder the terms:
132.25 + 23x + x2 = -124 + 132.25

Combine like terms: -124 + 132.25 = 8.25
132.25 + 23x + x2 = 8.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 11.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 11.5 = 2.872281323

Simplifying
x + 11.5 = 2.872281323

Reorder the terms:
11.5 + x = 2.872281323

Solving
11.5 + x = 2.872281323

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 = 2.872281323 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 2.872281323 + -11.5
x = 2.872281323 + -11.5

Combine like terms: 2.872281323 + -11.5 = -8.627718677
x = -8.627718677

Simplifying
x = -8.627718677

Subproblem 2
x + 11.5 = -2.872281323

Simplifying
x + 11.5 = -2.872281323

Reorder the terms:
11.5 + x = -2.872281323

Solving
11.5 + x = -2.872281323

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 = -2.872281323 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -2.872281323 + -11.5
x = -2.872281323 + -11.5

Combine like terms: -2.872281323 + -11.5 = -14.372281323
x = -14.372281323

Simplifying
x = -14.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.627718677, -14.372281323}