x^2-39x-120=0

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Solution for x^2-39x-120=0 equation: 


Simplifying
x2 + -39x + -120 = 0

Reorder the terms:
-120 + -39x + x2 = 0

Solving
-120 + -39x + 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 + -39x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -39x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -39x + x2 = 0 + 120
-39x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-39x + x2 = 120

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = 120 + 380.25

Reorder the terms:
380.25 + -39x + x2 = 120 + 380.25

Combine like terms: 120 + 380.25 = 500.25
380.25 + -39x + x2 = 500.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 500.25

Calculate the square root of the right side: 22.366269246

Break this problem into two subproblems by setting 
(x + -19.5) equal to 22.366269246 and -22.366269246.


Subproblem 1
x + -19.5 = 22.366269246

Simplifying
x + -19.5 = 22.366269246

Reorder the terms:
-19.5 + x = 22.366269246

Solving
-19.5 + x = 22.366269246

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = 22.366269246 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = 22.366269246 + 19.5
x = 22.366269246 + 19.5

Combine like terms: 22.366269246 + 19.5 = 41.866269246
x = 41.866269246

Simplifying
x = 41.866269246


Subproblem 2
x + -19.5 = -22.366269246

Simplifying
x + -19.5 = -22.366269246

Reorder the terms:
-19.5 + x = -22.366269246

Solving
-19.5 + x = -22.366269246

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = -22.366269246 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = -22.366269246 + 19.5
x = -22.366269246 + 19.5

Combine like terms: -22.366269246 + 19.5 = -2.866269246
x = -2.866269246

Simplifying
x = -2.866269246


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.866269246, -2.866269246}

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