x^2-23x-120=0

Solution for x^2-23x-120=0 equation:

Simplifying
x2 + -23x + -120 = 0

Reorder the terms:
-120 + -23x + x2 = 0

Solving
-120 + -23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -23x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -23x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -23x + x2 = 0 + 120
-23x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-23x + x2 = 120

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 = 120 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 120 + 132.25

Combine like terms: 120 + 132.25 = 252.25
132.25 + -23x + x2 = 252.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 252.25

Calculate the square root of the right side: 15.882380174

Break this problem into two subproblems by setting 
(x + -11.5) equal to 15.882380174 and -15.882380174.

Subproblem 1
x + -11.5 = 15.882380174

Simplifying
x + -11.5 = 15.882380174

Reorder the terms:
-11.5 + x = 15.882380174

Solving
-11.5 + x = 15.882380174

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 = 15.882380174 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 15.882380174 + 11.5
x = 15.882380174 + 11.5

Combine like terms: 15.882380174 + 11.5 = 27.382380174
x = 27.382380174

Simplifying
x = 27.382380174

Subproblem 2
x + -11.5 = -15.882380174

Simplifying
x + -11.5 = -15.882380174

Reorder the terms:
-11.5 + x = -15.882380174

Solving
-11.5 + x = -15.882380174

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 = -15.882380174 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -15.882380174 + 11.5
x = -15.882380174 + 11.5

Combine like terms: -15.882380174 + 11.5 = -4.382380174
x = -4.382380174

Simplifying
x = -4.382380174

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.382380174, -4.382380174}