99.8+99.8*(1+X)+99.8*(1+X)*(1+X)=120.8

Solution for 99.8+99.8*(1+X)+99.8*(1+X)*(1+X)=120.8 equation:

Simplifying
99.8 + 99.8(1 + X) + 99.8(1 + X)(1 + X) = 120.8
99.8 + (1 * 99.8 + X * 99.8) + 99.8(1 + X)(1 + X) = 120.8
99.8 + (99.8 + 99.8X) + 99.8(1 + X)(1 + X) = 120.8

Multiply (1 + X) * (1 + X)
99.8 + 99.8 + 99.8X + 99.8(1(1 + X) + X(1 + X)) = 120.8
99.8 + 99.8 + 99.8X + 99.8((1 * 1 + X * 1) + X(1 + X)) = 120.8
99.8 + 99.8 + 99.8X + 99.8((1 + 1X) + X(1 + X)) = 120.8
99.8 + 99.8 + 99.8X + 99.8(1 + 1X + (1 * X + X * X)) = 120.8
99.8 + 99.8 + 99.8X + 99.8(1 + 1X + (1X + X2)) = 120.8

Combine like terms: 1X + 1X = 2X
99.8 + 99.8 + 99.8X + 99.8(1 + 2X + X2) = 120.8
99.8 + 99.8 + 99.8X + (1 * 99.8 + 2X * 99.8 + X2 * 99.8) = 120.8
99.8 + 99.8 + 99.8X + (99.8 + 199.6X + 99.8X2) = 120.8

Reorder the terms:
99.8 + 99.8 + 99.8 + 99.8X + 199.6X + 99.8X2 = 120.8

Combine like terms: 99.8 + 99.8 = 199.6
199.6 + 99.8 + 99.8X + 199.6X + 99.8X2 = 120.8

Combine like terms: 199.6 + 99.8 = 299.4
299.4 + 99.8X + 199.6X + 99.8X2 = 120.8

Combine like terms: 99.8X + 199.6X = 299.4X
299.4 + 299.4X + 99.8X2 = 120.8

Solving
299.4 + 299.4X + 99.8X2 = 120.8

Solving for variable 'X'.

Reorder the terms:
299.4 + -120.8 + 299.4X + 99.8X2 = 120.8 + -120.8

Combine like terms: 299.4 + -120.8 = 178.6
178.6 + 299.4X + 99.8X2 = 120.8 + -120.8

Combine like terms: 120.8 + -120.8 = 0.0
178.6 + 299.4X + 99.8X2 = 0.0

Begin completing the square.  Divide all terms by
99.8 the coefficient of the squared term: 

Divide each side by '99.8'.
1.789579158 + 3X + X2 = 0

Move the constant term to the right:

Add '-1.789579158' to each side of the equation.
1.789579158 + 3X + -1.789579158 + X2 = 0 + -1.789579158

Reorder the terms:
1.789579158 + -1.789579158 + 3X + X2 = 0 + -1.789579158

Combine like terms: 1.789579158 + -1.789579158 = 0.000000000
0.000000000 + 3X + X2 = 0 + -1.789579158
3X + X2 = 0 + -1.789579158

Combine like terms: 0 + -1.789579158 = -1.789579158
3X + X2 = -1.789579158

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = -1.789579158 + 2.25

Reorder the terms:
2.25 + 3X + X2 = -1.789579158 + 2.25

Combine like terms: -1.789579158 + 2.25 = 0.460420842
2.25 + 3X + X2 = 0.460420842

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 0.460420842

Calculate the square root of the right side: 0.678543176

Break this problem into two subproblems by setting 
(X + 1.5) equal to 0.678543176 and -0.678543176.

Subproblem 1
X + 1.5 = 0.678543176

Simplifying
X + 1.5 = 0.678543176

Reorder the terms:
1.5 + X = 0.678543176

Solving
1.5 + X = 0.678543176

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = 0.678543176 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 0.678543176 + -1.5
X = 0.678543176 + -1.5

Combine like terms: 0.678543176 + -1.5 = -0.821456824
X = -0.821456824

Simplifying
X = -0.821456824

Subproblem 2
X + 1.5 = -0.678543176

Simplifying
X + 1.5 = -0.678543176

Reorder the terms:
1.5 + X = -0.678543176

Solving
1.5 + X = -0.678543176

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = -0.678543176 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -0.678543176 + -1.5
X = -0.678543176 + -1.5

Combine like terms: -0.678543176 + -1.5 = -2.178543176
X = -2.178543176

Simplifying
X = -2.178543176

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.821456824, -2.178543176}