x^2+x-120=

Solution for x^2+x-120= equation:

Simplifying
x2 + x + -120 = 0

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

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 120 + 0.25

Reorder the terms:
0.25 + x + x2 = 120 + 0.25

Combine like terms: 120 + 0.25 = 120.25
0.25 + x + x2 = 120.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.9658561 and -10.9658561.

Subproblem 1
x + 0.5 = 10.9658561

Simplifying
x + 0.5 = 10.9658561

Reorder the terms:
0.5 + x = 10.9658561

Solving
0.5 + x = 10.9658561

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 10.9658561 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 10.9658561 + -0.5
x = 10.9658561 + -0.5

Combine like terms: 10.9658561 + -0.5 = 10.4658561
x = 10.4658561

Simplifying
x = 10.4658561

Subproblem 2
x + 0.5 = -10.9658561

Simplifying
x + 0.5 = -10.9658561

Reorder the terms:
0.5 + x = -10.9658561

Solving
0.5 + x = -10.9658561

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -10.9658561 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -10.9658561 + -0.5
x = -10.9658561 + -0.5

Combine like terms: -10.9658561 + -0.5 = -11.4658561
x = -11.4658561

Simplifying
x = -11.4658561

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.4658561, -11.4658561}