0=x^2-10.1-198x

Solution for 0=x^2-10.1-198x equation:

Simplifying
0 = x2 + -10.1 + -198x

Reorder the terms:
0 = -10.1 + -198x + x2

Solving
0 = -10.1 + -198x + x2

Solving for variable 'x'.

Combine like terms: 0 + 10.1 = 10.1
10.1 + 198x + -1x2 = -10.1 + -198x + x2 + 10.1 + 198x + -1x2

Reorder the terms:
10.1 + 198x + -1x2 = -10.1 + 10.1 + -198x + 198x + x2 + -1x2

Combine like terms: -10.1 + 10.1 = 0.0
10.1 + 198x + -1x2 = 0.0 + -198x + 198x + x2 + -1x2
10.1 + 198x + -1x2 = -198x + 198x + x2 + -1x2

Combine like terms: -198x + 198x = 0
10.1 + 198x + -1x2 = 0 + x2 + -1x2
10.1 + 198x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10.1 + 198x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10.1 + -198x + x2 = 0

Move the constant term to the right:

Add '10.1' to each side of the equation.
-10.1 + -198x + 10.1 + x2 = 0 + 10.1

Reorder the terms:
-10.1 + 10.1 + -198x + x2 = 0 + 10.1

Combine like terms: -10.1 + 10.1 = 0.0
0.0 + -198x + x2 = 0 + 10.1
-198x + x2 = 0 + 10.1

Combine like terms: 0 + 10.1 = 10.1
-198x + x2 = 10.1

The x term is -198x.  Take half its coefficient (-99).
Square it (9801) and add it to both sides.

Add '9801' to each side of the equation.
-198x + 9801 + x2 = 10.1 + 9801

Reorder the terms:
9801 + -198x + x2 = 10.1 + 9801

Combine like terms: 10.1 + 9801 = 9811.1
9801 + -198x + x2 = 9811.1

Factor a perfect square on the left side:
(x + -99)(x + -99) = 9811.1

Calculate the square root of the right side: 99.050996966

Break this problem into two subproblems by setting 
(x + -99) equal to 99.050996966 and -99.050996966.

Subproblem 1
x + -99 = 99.050996966

Simplifying
x + -99 = 99.050996966

Reorder the terms:
-99 + x = 99.050996966

Solving
-99 + x = 99.050996966

Solving for variable 'x'.

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

Add '99' to each side of the equation.
-99 + 99 + x = 99.050996966 + 99

Combine like terms: -99 + 99 = 0
0 + x = 99.050996966 + 99
x = 99.050996966 + 99

Combine like terms: 99.050996966 + 99 = 198.050996966
x = 198.050996966

Simplifying
x = 198.050996966

Subproblem 2
x + -99 = -99.050996966

Simplifying
x + -99 = -99.050996966

Reorder the terms:
-99 + x = -99.050996966

Solving
-99 + x = -99.050996966

Solving for variable 'x'.

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

Add '99' to each side of the equation.
-99 + 99 + x = -99.050996966 + 99

Combine like terms: -99 + 99 = 0
0 + x = -99.050996966 + 99
x = -99.050996966 + 99

Combine like terms: -99.050996966 + 99 = -0.050996966
x = -0.050996966

Simplifying
x = -0.050996966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {198.050996966, -0.050996966}