0=120+x+x^2

Solution for 0=120+x+x^2 equation:

Simplifying
0 = 120 + x + x2

Solving
0 = 120 + x + x2

Solving for variable 'x'.

Combine like terms: 0 + -120 = -120
-120 + -1x + -1x2 = 120 + x + x2 + -120 + -1x + -1x2

Reorder the terms:
-120 + -1x + -1x2 = 120 + -120 + x + -1x + x2 + -1x2

Combine like terms: 120 + -120 = 0
-120 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
-120 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-120 + -1x + -1x2 = 0 + x2 + -1x2
-120 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-120 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(120 + x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(120 + x + x2)' equal to zero and attempt to solve:

Simplifying
120 + x + x2 = 0

Solving
120 + x + x2 = 0

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 = -119.75
0.25 + x + x2 = -119.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -119.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.