99.8+99.8*(1+X)+99.8*(1+X)*(1+X)=362.53

Solution for 99.8+99.8*(1+X)+99.8*(1+X)*(1+X)=362.53 equation:

Simplifying
99.8 + 99.8(1 + X) + 99.8(1 + X)(1 + X) = 362.53
99.8 + (1 * 99.8 + X * 99.8) + 99.8(1 + X)(1 + X) = 362.53
99.8 + (99.8 + 99.8X) + 99.8(1 + X)(1 + X) = 362.53

Multiply (1 + X) * (1 + X)
99.8 + 99.8 + 99.8X + 99.8(1(1 + X) + X(1 + X)) = 362.53
99.8 + 99.8 + 99.8X + 99.8((1 * 1 + X * 1) + X(1 + X)) = 362.53
99.8 + 99.8 + 99.8X + 99.8((1 + 1X) + X(1 + X)) = 362.53
99.8 + 99.8 + 99.8X + 99.8(1 + 1X + (1 * X + X * X)) = 362.53
99.8 + 99.8 + 99.8X + 99.8(1 + 1X + (1X + X2)) = 362.53

Combine like terms: 1X + 1X = 2X
99.8 + 99.8 + 99.8X + 99.8(1 + 2X + X2) = 362.53
99.8 + 99.8 + 99.8X + (1 * 99.8 + 2X * 99.8 + X2 * 99.8) = 362.53
99.8 + 99.8 + 99.8X + (99.8 + 199.6X + 99.8X2) = 362.53

Reorder the terms:
99.8 + 99.8 + 99.8 + 99.8X + 199.6X + 99.8X2 = 362.53

Combine like terms: 99.8 + 99.8 = 199.6
199.6 + 99.8 + 99.8X + 199.6X + 99.8X2 = 362.53

Combine like terms: 199.6 + 99.8 = 299.4
299.4 + 99.8X + 199.6X + 99.8X2 = 362.53

Combine like terms: 99.8X + 199.6X = 299.4X
299.4 + 299.4X + 99.8X2 = 362.53

Solving
299.4 + 299.4X + 99.8X2 = 362.53

Solving for variable 'X'.

Reorder the terms:
299.4 + -362.53 + 299.4X + 99.8X2 = 362.53 + -362.53

Combine like terms: 299.4 + -362.53 = -63.13
-63.13 + 299.4X + 99.8X2 = 362.53 + -362.53

Combine like terms: 362.53 + -362.53 = 0.00
-63.13 + 299.4X + 99.8X2 = 0.00

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

Divide each side by '99.8'.
-0.6325651303 + 3X + X2 = 0.0

Move the constant term to the right:

Add '0.6325651303' to each side of the equation.
-0.6325651303 + 3X + 0.6325651303 + X2 = 0.0 + 0.6325651303

Reorder the terms:
-0.6325651303 + 0.6325651303 + 3X + X2 = 0.0 + 0.6325651303

Combine like terms: -0.6325651303 + 0.6325651303 = 0.0000000000
0.0000000000 + 3X + X2 = 0.0 + 0.6325651303
3X + X2 = 0.0 + 0.6325651303

Combine like terms: 0.0 + 0.6325651303 = 0.6325651303
3X + X2 = 0.6325651303

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 = 0.6325651303 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 0.6325651303 + 2.25

Combine like terms: 0.6325651303 + 2.25 = 2.8825651303
2.25 + 3X + X2 = 2.8825651303

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 2.8825651303

Calculate the square root of the right side: 1.697811865

Break this problem into two subproblems by setting 
(X + 1.5) equal to 1.697811865 and -1.697811865.

Subproblem 1
X + 1.5 = 1.697811865

Simplifying
X + 1.5 = 1.697811865

Reorder the terms:
1.5 + X = 1.697811865

Solving
1.5 + X = 1.697811865

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 = 1.697811865 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 1.697811865 + -1.5
X = 1.697811865 + -1.5

Combine like terms: 1.697811865 + -1.5 = 0.197811865
X = 0.197811865

Simplifying
X = 0.197811865

Subproblem 2
X + 1.5 = -1.697811865

Simplifying
X + 1.5 = -1.697811865

Reorder the terms:
1.5 + X = -1.697811865

Solving
1.5 + X = -1.697811865

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 = -1.697811865 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -1.697811865 + -1.5
X = -1.697811865 + -1.5

Combine like terms: -1.697811865 + -1.5 = -3.197811865
X = -3.197811865

Simplifying
X = -3.197811865

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.197811865, -3.197811865}