198=(x+13)(x+14)

Solution for 198=(x+13)(x+14) equation:

Simplifying
198 = (x + 13)(x + 14)

Reorder the terms:
198 = (13 + x)(x + 14)

Reorder the terms:
198 = (13 + x)(14 + x)

Multiply (13 + x) * (14 + x)
198 = (13(14 + x) + x(14 + x))
198 = ((14 * 13 + x * 13) + x(14 + x))
198 = ((182 + 13x) + x(14 + x))
198 = (182 + 13x + (14 * x + x * x))
198 = (182 + 13x + (14x + x2))

Combine like terms: 13x + 14x = 27x
198 = (182 + 27x + x2)

Solving
198 = 182 + 27x + x2

Solving for variable 'x'.

Combine like terms: 198 + -182 = 16
16 + -27x + -1x2 = 182 + 27x + x2 + -182 + -27x + -1x2

Reorder the terms:
16 + -27x + -1x2 = 182 + -182 + 27x + -27x + x2 + -1x2

Combine like terms: 182 + -182 = 0
16 + -27x + -1x2 = 0 + 27x + -27x + x2 + -1x2
16 + -27x + -1x2 = 27x + -27x + x2 + -1x2

Combine like terms: 27x + -27x = 0
16 + -27x + -1x2 = 0 + x2 + -1x2
16 + -27x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -27x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 27x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 27x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 27x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 27x + x2 = 0 + 16
27x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
27x + x2 = 16

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = 16 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 16 + 182.25

Combine like terms: 16 + 182.25 = 198.25
182.25 + 27x + x2 = 198.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 198.25

Calculate the square root of the right side: 14.08012784

Break this problem into two subproblems by setting 
(x + 13.5) equal to 14.08012784 and -14.08012784.

Subproblem 1
x + 13.5 = 14.08012784

Simplifying
x + 13.5 = 14.08012784

Reorder the terms:
13.5 + x = 14.08012784

Solving
13.5 + x = 14.08012784

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 14.08012784 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 14.08012784 + -13.5
x = 14.08012784 + -13.5

Combine like terms: 14.08012784 + -13.5 = 0.58012784
x = 0.58012784

Simplifying
x = 0.58012784

Subproblem 2
x + 13.5 = -14.08012784

Simplifying
x + 13.5 = -14.08012784

Reorder the terms:
13.5 + x = -14.08012784

Solving
13.5 + x = -14.08012784

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -14.08012784 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -14.08012784 + -13.5
x = -14.08012784 + -13.5

Combine like terms: -14.08012784 + -13.5 = -27.58012784
x = -27.58012784

Simplifying
x = -27.58012784

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.58012784, -27.58012784}